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INTELLECTUAL  ARITHMETIC ; 

ON  THE  INDUCTIVE  PLAN. 

BEING 

A  SEQUEL  TO  THE  PROGRESSIVE  PRIMARY  ARITHMETIC,  CONTAININQ 

MANY  ORIGINAL  FORMS   OF  ANALYSIS   APPLICABLE  TO  A 

GREAT   VARIETY   OF   PRACTICAL  QUESTIONS, 

AND    DESIGNED    FOR 

THE    MORE    ADVANCED    CLASSES 

IN 

COMMON     SCHOOLS     AND     ACADEMIES. 

EDITED    BY 

DAIS^IEL  W.  FISH,  A.M. 

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1870. 


KO  B  IN  S  O  N'S 


^ 


Tlie  most  Complete,  most  Practical,  and  most  Scientific  Series 
of  Mathematical  Text-Books  ever  issued  in  this  country. 


» »  »  » » 

Kobinson's  Progressive  Table  Book,  -       -       .       -       - 
Rooinson's  Progressive  Primary  Arithmetic, - 
Robinson's  Progressive  Intellectual  Arithmetic,   - 
Robinson's  Rudiments  of  "Written  Arithmetic, 
Robinson's  Progressive  Practical  Arithmetic, 
Robinson's  Key  to  Practical  Arithmetic,  -       -       -       - 
Robinson's  Progressive   Higher  Arithmetic,    -       -       - 
Robinson's  Key  to  Higher  Arithmetic,     -       -       -       -       - 

Robinson's  Arithmetical  Examples, 

Robinson's  New   JEllementary  Algebra, 

Robinson's  Key  to  Elementary  Algebra,  -       -       -       -       - 

Robinson's  University  Algebra,   ------- 

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Robinson's  Diflferen.  and  Int.  Calculus,  (in  prepai?tion,)- 

Kiddle's  New  Elementary  Astronomy, 

Robinson's  University  Astronomy, 

Robinson's  Mathematical  Operations,        .       -       -       -       - 

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Sections  and  Analytical  Geometry,      .      -      -      -      - 


Entered,  according  to  Act  of  Congress,  in  the  year  1S58, 
and  again  in  the  year  1S63,  by 

DANIEL    W.    FISH,    A.M., 

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District  of  New  York. 


PREFACE. 


The  importance,  and  the  practical  benefit  to  be  derived  from  the 
studv  of  Intellectual  Arithmetic,  not  only  as  a  prejjaration  for  busi- 
ness' life,  but  as  a  means  of  developing  and  slrengthenmg  the 
thinking  and  reasoning  powers,  and  of  thorough  mental  culture, 
can  not"  be  over-estimated.  Not  only  is  it  a  necessary  study  tor 
young  pupils,  but  indispensable  to  the  more  advanced  student,  as 
a  preparation  for  the  prompt  and  accurate  business  man.  And  it 
is  believed  that,  as  a  general  rule,  the  most  critical,  correct,  and 
ready  students  of  mathematics  are  those  who  have  been  most 
thoroughlv  drilled  in  intellectual  arithmetic. 

This  work  has  been  prepared  more  especially  for  advanced  classes, 
and  is  designed  for  those  who  have  first  been  well  taught  in  the 
primary  book,  and  for  such  as  are  pursuing  the  study  ot  written 
arithmetic,  or  algebra,  and  who  have  never  been  thoroughly  exer- 
cised in  this  branch  of  study. 

Only  a  few  of  the  manv  points  of  difference  between  this  and 
other  similar  works,  and  which,  it  is  believed,  renders  tins  superior 
to  them,  will  be  referred  to. 

It  is  more  complete,  comprehensive,  and  progressive  in  its  char- 
acter. The  arrangement  and  classification  are  more  strictly  sys- 
tematic, and  in  accordance  with  the  natural  order  of  mathematical 
science.  The  development  of  principles,  and  their  a j) plications, 
are  shown  by  a  more  numerous  selection,  and  greater  yarietv  of 
appropriate  examples,  progressively  arranged,  commencing  with 
those  that  are  simple  and  easy,  and  advancing  to  those  more  com- 
plex and  difficult. 

At  intervals,  and  especially  in  the  closing  sections  of  each  chap- 
ter, examples  are  given  containing  such  a  combination  of  principles, 
and  forms  of  analysis,  as  to  require  a  knowledge  of  almost  every 
principle  previously  taught,  thus  affording  the  pupil  a  thorough 
review,  as  well  as  requiring  him  to  classify  his  knowledge  of  what 
he  has  been  over. 

One  of  the  most  important,  and,  it  is  thought,  one  of  the  most 
original  and  useful  features  of  this  work,  is  the  full,  concise,  and 
uniform  system  of  Analysis  it  contains,  —  the  result  of  long  expc 
rience  in  the  school-room. 

Particular  attention  is  invited  to  the  subjects  of  Fractions,  Per' 
centage,  and  Interest ;  their  treatment  is  peculiar,  and  adapted  to 
obviate  many  of  the  difficulties,  and  greatly  abbreviate  most  of  the 
operations  in  them. 

(S) 


4  PREFACE. 

The  chapter  of  Miscellaneous  Examples  will  afford  a  valuable 
and  thorough  drill  to  the  advanced  student  of  arithmetic  ov  alge- 
bra. They  contain  a  great  variety  of  principles,  and  while  they 
may  be  considered  difhcult,  yet  the  full  analysis  given  of  every 
principle,  and  the  selection  of  numbers  so  adapted  to  the  conditions 
of  the  question  as  to  produce  results  free  from  large  and  difficult 
fractions,  will  render  a  mental  solution  of  them  comparatively  easy. 

In  conclusion,  we  may  be  allowed  to  express  the  belief,  that 
in  this  work  the  thorough  teacher  Avill  find  a  desideratum  long 
sought  in  this  department  of  science, — the  means  of  mental  dis- 
cipline and  development  such  as  has  been  furnished  by  no  similar 

treatise. 

THE  AUTHOR. 


SUGGESTIONS  TO  TEACHERS. 

Pupils  of  nearly  the  same  degree  of  advancement  should  be 
classed  together.  Regular  exercises  should  be  assigned  to  the 
class,  and  sufficient  time  allowed  them  to  thoroughly  examine 
their  lesson  before  being  called  upon  to  recite. 

The  use  of  the  book  at  the  time  of  recitation  should  be  strictly 
prohibited,  except,  perhaps,  in  some  of  the  more  difficult  lessons 
in  the  latter  part  of  the  work. 

Each  example  should  be  read  but  once,  slowhj  and  distinctly, 
the  pupils  called  upon  promiscuously,  who  should  arise,  stand 
erect,  repeat  the  example,  and  then  give  the  analysis.  This  will 
secure  close  attention. 

Every  question  should  be  clearly  and  tliorougldy  analyzed,  and 
the  pupil  required  to  adhere  strictly  to  t}\e  forms  of  solution  given, 
unless  better  ones  can  be  substituted ;  and  in  no  case  should  he 
be  allowed  to  omit  the  conclusion,  commencing  with  "  Therefore." 

The  class  should  be  encouraged  to  detect  and  correct  errors  in 
statement  or  analysis,  to  criticise  and  make  proper  inquiries,  all 
of  which  should  be  signaled  by  the  uplifted  hand. 

It  is  suggested  that  the  class  be  occasionally  exercised  upon 
"  Ringing  the  Changes,"  as  explained  in  the  Appendix,  and  which 
niay  be  applied  to  a  great  number  and  variety  of  exami)les.  It 
will  not  only  afibrd  a  valuable  diill,  but  a  pleasant  and  enlivening 
exercise. 


INTELLECTUAL    ARITHMETIC. 


CHAPTER  I. 

ADDITION. 

1.  1.  James  had  1  cent,  and  his  father  gave  him 
1  more  ;  how  many  had  he  then  ? 

2.  If  a  slate  pencil  cost  2  cents,  and  a  steel  pen 
1  cent,  how  many^  cents  will  both  cost  ? 

3.  George  spent  2  cents  for  candy,  and  had  2  cents 
left ;  how  many  cents  had  he  a,t  first  ? 

4.  A  farmer  sold  a  calf  for  3  dollars,  and  a  pig; 
for  2  dollars ;  how  many  dollars  did  he  receive  foi.' 
both? 

5.  Mary  gave  2  cents  for  some  tape,  and  5  cents 
for  a  thimble  ;  how  many  cents  did  she  give  for  both  ? 

6.  Martin  gave  John  3  apples,  and  kept  4  for  him- 
self ;  how  many  apples  had  he  at  first  ? 

7.  There  are  4  books  on  one  desk,  and  2  books 
on  another ;  how  many  books  on  both  desks  ? 

8.  If  a  lemon  cost  3  cents,  and  an  orange  5  cents, 
how  many  cents  do  both  cost  ? 

9.  In  a  certain  class  there  are  5  girls  and  4  boys ; 
how  many  pupils  in  the  class  ? 

10.  Samuel  had  3  marbles,  and  his  brother  gave 
him  3  more  ;  how  manv  did  he  then  have  ? 

11.  Bought  a  barrel  of  apples  for  2  dollars,  and  a 

cord  of  wood  for  4  dollars ;  how  many  dollars  did 

both  cost  ? 

1*  (5) 


6  INTELLECTUAL  ARITHMETIC.                        [S. 

3.     1.  1  and  1  are  how  many  ? 

2.  1  and  2  are  how  many  ? 

3.  2  and  2  are  how  many  ? 

4.  2  and  3.  are  how  many^ 

5.  2  and  4  are  how  many  ? 

6.  2  and  Jx^  are  how  many  ? 

7.  2  and  6  are  how  many  ? 

8.  2  and  7  are  how  many  ? 

9.  2  and  8  are  how  many  ? 
IjP.  2  and  9  are  how  many  ? 

11.  3  and  3  are  how  many  ? 

12.  3  and  4  are  how  many  ? 

13.  3  and  5  are  how  many  ? 

14.  3  and  6  are  how  many  ? 

15.  3  and  1  are  how  many  ? 

16.  3  and  8  are  how  many  ? 

17.  3  and  9  are  how  many  ?     .| 

18.  3  and  1$^  ar(^  how  many  ?  >«8|\ 

19.  4  and  2  are  how  many?.. 

20.  4  and  3  are  how  many  ? 

21.  4  and  4  are  how  many  ? 

22.  4  and  5  are  how  many  ? 

23.  4  and  6  are  how  many  ? 

24.  4  and  7  are  how  many  ? 

25.  4  and  8  are  how  many  ? 

26.  4  and  9  are  how  many  ? 

27.  4  and  10  are  how  many  ? 

28.  5  and  1  are  how  many  ? 

29.  5  and  2  are  how  many  ? 

30.  5  and  3  are  how  many  ? 

31.  5  and  4  are  how  many  ? 

32.  5  and  5  are  how  many  ? 

33.  5  and  6  are  how  many  ? 

34.  5  and  7  are  how  many  ? 

35.  5  and  8  are  how  many  ? 
86.  5  and  9*' are  how  many? 


1?.J  INTELLECTUAL   ARITHMETIC.  7 

3.  1.  A  man  bought  a  calf  for  7  dollars,  and 
sold  it  for  3  dollars  more  than  he  gave  for  it ;  how 
much  did  he  sell  it  for  ? 

2.  Bought  a  barrel  of  cider  for  2  dollars,  and  20 
bushels  of  apples  for  8  dollars  ;  how  many  dollars 
did  the  whole  cost  ? 

3.  If  a  coat  cost  10  dollars,  and  a  pair  of  panta- 
loons 5  dollars,  what  will  be  the  cost  of  both  ? 

4.  A  merchant  bought  4  boxes  of  black  tea,  and 
7  boxes  of  green  tea ;  how  many  boxes  did  he  buy 
of  both  kinds  ? 

5.  A  farmer  sold  5  sheep  to  one  man,  and  9  to 
another  ;  how  many  did  he  sell  to  both  ? 

6.  Ralph  walked  4  miles  and  rode  10  miles  ;  how 
many  miles  did  he  go  ? 

7.  Philip  answered  8  questions  in  geogi^aphy,  and 
Oliver  5  ;  how  many  questions  did  both  answer  ? 

8.  If  a  quart  of  chestnuts  cost  10  cents,  and  a 
quart  of  walnuts  4  cents,  what  will  be  the  cost  of 
one  quart  of  both  ? 

are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 


9. 

6 

and 

3 

10. 

6 

and 

4 

11. 

6 

and 

5 

12. 

G 

and 

6 

13. 

6 

and 

7 

14. 

6 

and 

8 

15. 

6 

and 

9 

16. 

6 

and 

10 

17. 

T 

and  ^ 

18. 

7 

• 

anc. 

5 

19. 

7 

and 

6 

20. 

and 

7 

21. 

7 

and 

8 

22. 

7 

and 

9 

23. 

7 

and 

10 

24. 

8 

and 

3 

8  INTELLECTUAL   ARITHMETIC.  t"** 

25.  8  and    4  are  how  many? 

26.  8  and     5  are  how  many  ? 

27.  8  and     6  are  how  many  ? 

28.  8  and     7  are  how  many  ? 

29.  8  and     8  are  how  many  ? 

30.  8  and     9  are  how  many  ? 

31.  8  and  10  are  how  many  ? 

32.  9  and     4  are  how  many? 

33.  9  and     5  are  how  many? 

34.  9  and     6  are  how  many? 

35.  9  and     7  are  how  many  ? 

36.  9  and     8  are  how  many? 

37.  9  and     9  are  how  many  ? 

38.  9  and  10  are  how  many? 

39.  10  and     4  are  how  many? 

40.  10  and     5  are  how  many  ? 

41.  10  and     6  are  how  many? 


4.  1.  Eli  paid  9  shillings  for  a  pair  of  skates, 
and  6  shillings  for  a  cap ;  how  many  shillings  did  he 
pay  for  both  ? 

Analysis.  Since  Mi  paid  9  shillings  for  a  pair  of 
skates,  and  6  shillings  for  a  cap,  he  paid  for  both,  the 
sum  of  9  shillings  and  6  shillings.  The  sum  of  9  shil- 
lings and  6  shillings  is  15  shillings.  Therefore,  he  paid 
35  shillings  for  both, 

2.  A  farmer  sold  some  oats  for  7  dollars,  and  a 
ton  of  hay  for  9  dollars  ;  how  many  dollars  did  he 
receive  for  both  ? 

3.  Paid  8  cents  for  some  raisins,  and  6  cents  for 
some  cloves  ;  how  manj^  cents  did  both  cost  ? 

4.  Nancy  is  10  years  old ;  how  old  will  she  be 
5  years  from  this  time  ? 

5.  A  lady  paid  7  dollars  for  a  shawl,  and  6  dol- 
lars for  a  dress  \  ^hat  was  the  cost  of  both  ? 


5.]  INTELLECTUAL   ARITHMETIC.  ^  9 

6.  There  are  9  boys  in  one  class,  and  7  in  anoth- 
er ;  how  many  in  both  classes  ? 

7.  Margaret  has  8  flower  pots  in  one  room,  and  5 
in  another ;  how  many  has  she  in  the  two  rooms  ? 

8.  If  you  read  10  pages  to-day,  and  7  pages  to- 
morrow, how  many  will  you  read  in  both  days  ? 

9.  If  a  firkin  of  butter  is  worth  9  dollars,  and 
two  cords  of  wood  are  worth  8  dollars 5  what  are  both 
worth  ? 

10.  Myron  has  6  young  rabbits  and  4  old  ones ; 
how  many  rabbits  has  he  ? 

11.  Tiiere  are  10  biids  sitting  on  one  limb,  and 
9  on  another  ;  how  many  birds  on  both  limbs  ? 

12.  A  boy,  having  some  peaches  given  him,  put  8 
into  his  hat,  and  7  into  his  pockets ;  hovr  many 
peaches  were  given  him  ? 

13.  Edwin  found  6  ripe  pears  under  one  tree,  and 
8  under  another ;  how  many  pears  did  he  find  under 
both  trees  ? 

14.  In  one  yard  are  5  cows,  and  in  another  7 ; 
how  many  cows  in  both  yards  ? 

15.  If  you  work  8  examples  in  arithmetic  to-day, 
and  8  more  to-morrow,  how  many  will  you  work 
in  both  days  ? 

16.  Robert  gave  8  nuts  to  Henry,  and  kept  9  ;  how 
many  nuts  had  he  at  first  ? 


5. 


1. 

7 

and 

4 

are 

how 

many  ? 

2. 

9 

and 

7 

are 

how 

many  ? 

3. 

6 

anc. 

7 

are 

how 

many  ? 

4. 

5 

and 

9 

are 

low 

many  ? 

5. 

8 

and 

7 

are 

low 

many? 

6.  10     and     6     are  how  many  ? 

7.  9     and     6     are  how  many  ? 

8.  8     and     8     are  how  many  ? 


10  INTELLECTUAL   ARITHMETIC.  [5. 


9. 

6 

and  8 

10. 

7 

and  9 

11. 

8 

and  10 

12. 

11 

and  5 

13. 

13 

and  7 

14. 

14 

and  6 

15. 

12 

and  4 

16. 

15 

and  8 

17. 

9 

and  12 

18. 

IG 

and  8 

19. 

17 

and  10 

20. 

15 

and  11 

21. 

13 

and  12 

are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 


22.  How  many  are  2  and  2  ?     12  and  2  ?     22  and 
t2  ?     32  and  2  ?     42  and  2  ?     52  and  2  ?     62  and  2  ?^ 

72  and  2  ?     82  and  2  ?     92  and  2  ? 

23.  How  many  are  3  and  3  ?     13  and  3  ?     23  and 
3  ?     33  and  3  ?     43  and  3  ?     53  and  3  ?     63  and  3  ? 

73  and  3?     83  and  3?     93  and  3  ? 

24.  How  many  are  4  and  4  ?     14  and  4?     24  and 
4?     34  and  4?     44  and  4  ?     54  and  4  ?     64  and  4  ? 

74  and  4  ?     84  and  4  ?     94  and  4  ? 

25.  How  many  are  5  and  5  ?     15  and  5  ?     25  and 

5  ?#  35  and  5  ?  "  45  and  5  ?     55  and  5  ?     65  and  5  ? 
75 'and  5  ?     85  and  5  ?     95  and  5  ? 

26.  How  many  are  6  and  6  ?     16  and  6  ?     26  and 

6  ?     36  and  6  ?     46  and  6  ?     56  and  6  ?     66  and  6  ? 

76  and  6  ?     86  and  6  ?     96  and  6  ? 

27.  How  many  are  7  and  7  ?     17  and  7  ?     27  and 

7  ?     37  and  7  ?     47  and  7  ?     57  and  7  ?     67  and  7  ? 

77  and  7  ?     87  and  7  ?     97  and  7  ? 

28.  How  many  are  8  and  8  ?     18  and  8  ?     28  and 

8  ?     38  and  8  ?     48  and  8  ?     58  and  8  ?     68  and  8  ? 

78  and  8  ?     88  and  8  ?     98  and  8  ? 

29.  How  many  are  9  and  9  ?     19  and  9  ?     29  and 

9  ?     39  and  9  ?     49  and  9  ?     59  and  9  ?     69  and  9  ? 


6,]  INTELLECTUAL   ARITHMETIC.  11 

80.  How  many  are  8  and  7?  18  and  7  ?  28  and 

7  ?  38  and  7  ?  48  and  7  ?  58  and  7  ?  68  and  7.? 

78  and  7  ?  KS"  and  7  ?  98  and  7  ? 

31.  How  many  arc  10  and  10  ?  20  and  10  ?  30 
and  10?  40  and  10?  50  and  10  ?  60  and  10  ?  70 
and  10  ?  80  and  10  ?  90  and  10  ? 

32.  How  many  are  4  and  8  ?  14  and  8  ?  24  and 

8  ?  34  and  8  ?  44  and  8  ?  54  and  8  ?  64  and  8  ? 
74  and  8  ?  84  and  8  ?  94  and  8  ? 

33.  How  many  are  6  and  5  ?  16  and  5  ?  26  and 
5  ?  36  and  5  ?  46  and  5  ?  56  and  5  ?  66  and  5  ? 
76  and  5  ?  86  and  5  ?  96  and  5  ? 

34.  How  many  are  11  and  9  ?  21  and  9  ?  31  and 

9  ?  41  and  9  ?  51  and  9  ?  61  and  9  ?  71  and  9  ? 
81  and  9  ?  91  and  9  ? 

35.  How  many  are  9  and  7  ?  19  and  7  ?  29  and 

7  ?  39  and  7  ?  49  and  7  ?  59  and  7  ?  69  and  7  ? 

79  and  7  ?  89  and  7  ?  99  and  7  ? 

36.  How  many  are  4  and  8  ?  14  and  8  ?  24  and 

8  ?  34  and  8  ?  44  and  8  ?  54  and  8  ?  64  and  8  ? 
74  and  8  ?  84  and  8  ?  94  and  8  ? 

37.  How  many  are  3  and  10  ?  13  and  10  ?  23 
and  10  ?  33  and  10  ?  43  and  10  ?  53  and  10  ? 
63  and  10  ?  73  and  10  ?  83  and  10  ?  93  and  10  ? 


6.  Addition  is  the  process  of  uniting  several  numbers 
of  the  same  kind  into  one  equivalent  number.  The  result 
is  called  the  Stun  or  Amount.  The  sign  of  addition  is 
written  thus,  -|-,  and  is  called  j^^i^s.  AVhen  placed  between 
two  numbers  or  quantities,  it  shows  that  they  are  to  be 
added  together.  Thus,  5  -{-  3  -{-  2  signifies  that  5  and  3 
and  2  are  to  be  added  together,  and  is  read  Jive,  plus  three, 
plus  two. 

The  sign  of  equality  is  written  thus,  r=.  "When  placed 
between  two  numbers  or  quantities,  it  signifies  that  the 
latter  is  equal  to  the  former. 


12                          INTELLECTUAL  ARITHMETIC.                       [6 

1.  6+4+5  are  how  many? 

2.  9  -{-     7  -\-     S  are  how  many  ? 

3.  10  +     6  +     4  are  how  many? 

4.  13  +     8  +     6  are  how  many  ? 

5.  12  +  1^  +     ^  ^^®  l^ow  many  ? 

6.  11  +     ^  +     '^  ^i'Q  l^ow  many? 

7.  8  -f-  10  +     7  +  6     are  how  many  ? 

8.  34  +  25  are  how  many  ? 

Analysis.     ^45  many  as  the  sum  of  34:  and  25  ;  34 
is  composed  of  3  tens  and  4  units,  and  25  of  2  tens  and  5 

units ;  3  tens  and  2  tens  are  5  tens,  or  50,  and  4  units 
and  5  units  are  9  units,  which  added  to  50  marges  59. 
Therefore  34  +  25  «re  59. 

9.  46  +  31  are  how  many  ? 
10.  35  +  52  are  how  many  ? 
fr     40  +  30  +     6  are  how  many? 

12.  19  +  12  +     8  are  how  many  ? 

13.  60  +  'J'2  +     4  are  how  many? 

14.  48  +  30  +  10  are  how  many  ? 
0^5.     13  +  25  +     7  "4  are  how  many  ? 

16.  29  +  24  +  30  are  how  many  ? 

17.  64  +  40  +     9  are  how  many  ? 

18.  29  +  17  +  12  are  how  many  ? 

19.  7  +  37  +  26  are  how  many? 

20.  14  +  39  +     4  are  how  many? 

21.  48  +  31  +     9  are  how  many? 

22.  56  +  41  +  10  are  liow  many? 
'^'^      75  +  60  +  20  are  how  many  ? 

16  +  19  +  28  are  how  many  ? 

43  4-  37  +  15  are  how  many? 

84  +  75  +  20  are  how  many? 

68  +  52  +  45  are  liow  many? 

28.  35  +  77  +  51  arc  how  many  ? 

29.  80  +  95  +  12  are  how  many? 
80.     42  +  38  +  17  +  9     are  how  many  ? 


24. 
25. 

26. 

27. 


7.]  INTELLECTUAL   ARITHMETIC.  13 

7.  1.  A  man  gave  12  dollars  for  some  corn,  8 
dollars  for  a  ton  of  hay,  and  6  dollars  for  a  barrel  of 
flour  ;  how  much  did  he  pay  for  all  ? 

Analysis.  He  pc.z^.  the  sum  of  12  dollars,  8  dollars, 
and  G  dollars ;  12  and  8  are  20,  and  6  are  26  dollars. 
Therefore,  ^-c. 

2.  Emily  paid  12  shillings  for  a  dress,  10  shillings 
for  a  pair  of  shoes,  and  6  shillings  for  a  pair  of 
gloves  ;  what  was  the  cost  of  the  whole  ? 

3.  A  drover  had  15  horses  in  one  pasture,  13  in 
another,  and  9  in  another  ;  how  many  horses  had  he  ? 

4.  James  has  10  cents,  Henry  has  7,  and  John 
has  5  ;  how  many  cents  have  the  three  boys  ? 

5.  Bought  a  pound  of  candles  for  14  cents,  a 
pound  of  coffee  for  12  cents,  and  a  bar  of  soap  for 

9  cents  ;  w*hat  was  the  cost  of  the  whole  ? 

6.  In  a  shop  are  7  men,  9  boys,  and  6  .girls  at 
work ;  how  many  persons  at  work  in  the  shop  ? 

7.  A  lady  sold  10  pounds  of  butter  at  one  time, 
12  pounds  at  another,  and  8  pounds  at  another ; 
how  many  pounds  did  she  sell  in  all  ? 

8.  William  bought  an  arithmetic  for  15  cents, 
a  quire  of  paper  for  12  cents,  and  a  bottle  of  ink  for 
6  cents  ;  what  was  the  cost  of  the  whole  ? 

9.  Peter,  Dexter,  and  Irwin  gave  some  money  to 
a  beggar  ;  Peter  gave  him  10  cents,  Dexter  11  cents, 
and  Irwin  13  cents  ;  how  many  cents  did  they  all 
give  him  ? 

10.  In  a  certain  school  there  are  18  girls  and  24 
boys  ;  how  many  pupils  in  the  school  ? 

11.  A  man  bought  a  sleigh  for  20  dollars,  paid 

10  dollars  for  repairing  it,  and  6  dollars  for  paint- 
ing it ;  what  did  it  cost  liim  ? 

12.  Morgan  earned  25  cents  one  day,  and  32  the 
next ;  how  much  did  he  earn  in  both  days  ? 


14  INTELLECTUAL   ARITHMETIC.  [7. 

13.  A  farmer  sold  a  cow  for  22  dollars,  a  ton  of 
hay  for  11  dollars,  and  a  calf  for  7  dollars ;  what 
did  he  receive  for  all  ? 

14.  A  traveler  walked  3C  miles  one  day,  26 
miles  the  next,  and  21  miles  the  next;  how  many 
miles  did  he  travel  in  the  three  days  ? 

15.  One  day  Sarah  wrote  18  lines,  Maria  16,  and 
Carrie  15  ;  how  many  lines  did  they  all  write  ? 

16.  A  man  gave  60  dollars  for  a  horse,  23  dollars 
for  a  saddle,  and  9  dollars  for  a  bridle  ;  what  was  the 
cost  of  the  whole  ? 

17.  Rollin  received  36  new  cents  on  his  birthday, 
34  on  Christmas  day,  and  27  on  New  Year's  day ; 
how  many  cents  did  he  receive  ? 

18.  A  man  bought  a  piece  of  land  for  56  dollars, 
and  paid  25  dollars  for  fencing  it ;  for  how  much 
must  he  sell  it  to  gain  15  dollars  ? 

19.  Amasa,  going  into  the  orchard,  found  12  ripe 
apples  under  one  tree,  15  under  another,  11  under 
another,  and  9  under  another ;  how  many  apples  did 
he  find  under  the  four  trees  ? 

20.  A  grocer  bought  some  hams  for  20  dollars, 
some  oats  for  19  dollars,  some  fowls  for  16  dollars, 
and  five  barrels  of  apples  for  10  dollars ;  what 
did  he  pay  for  all  ? 

21.  A  miller  shipped  by  railroad  28  barrels  of 
flour  at  one  time,  37  at  another,  and  40  at  another ; 
how  many  barrels  did  he  ship  ? 

22.  If  Lucian  gave  45  cents  for  a  penknife,  15 
cents  for  some  paper,  12  cents  for  a  folder,  and  7 
cents  for  some  wafers,  what  did  the  whole  cost  him  ? 

23.  A  drover  bought  26  sheep  of  one  man,  30  of 
another,  37  of  another,  and  40  of  another  ;  how  many 
sheep  did  he  purcliase  ? 

24.  Bought  a  horse  for  75  dollars,  and  sold  him 
so  as  to  gain  25  dollars  ;  how  much  did  I  receive  for 
him  ? 


7.]  INTELLECTUAL  ARITHMETIC.  15 

25.  A  lady  went  shopping,  and  bought  a  silk  dress 
for  22  dollars,  a  muff  for  16  dollars,  a  shawl  for  14 
doHars,  and  had  7  dollars  left ;  how  much  money 
had  she  at  first  ? 

26.  Peleg  bought  a  knife  for  85  cents  ;  he  gave 
the  knife  and  12  cents  for  a  sled,  which  he  sold  so  as 
to  gain  10  cents  on  the  cost;  how  much  did  he 
receive  for  the  sled  ? 

27.  In  a  certain  orchard  are  31  apple  trees,  27 
peach  trees,  and  19  pear  trees ;  how  many  trees  in 
the  orchard  ? 

28.  A  farmer  raised  54  bushels  of  wheat,  6Q  bush- 
els of  oats,  and  40  bushels  of  corn  ;  how  many  bush- 
els of  grain  did  he  raise  ? 

29.  If  it  be  62  feet  from  the  ground  to  the  belfry 
of  a  church,  and  76  feet  from  the  belfry  to  the  top 
of  the  steeple,  how  high  is  the  top  of  the  steeple  from 
the  ground  ? 

30.  In  March  are  31  days,  in  April  30,  in  May  31 ; 
how  many  days  in  those  three  months  ? 

31.  If  a  farm  contain  83  acres  of  cleared  land 
and  25  acres  of  wood  land,  how  many  acres  are  in 
the  whole  farm  ? 

32.  The  distance  from  Boston  to  Worcester  is  44 
miles,  from  Worcester  to  Warren  29  miles,  and  from 
Warren  to  Springfield  25  miles ;  how  many  miles 
from  Boston  to  Springfield  ? 

33.  Batavia  is  37  miles  west  from  Rochester,  and 
81  miles  east  from  Buffalo  by  railroad ;  what  is  the 
distance  from  Rochester  to  Buffalo  ? 

34.  A  tailor  bought  three  pieces  of  cloth,  the  first 
containing  29  yards,  the  second  26  yards,  and  the 
third  25  yards  ;  how  many  yards  did  tlie  three  pieces 
contain  ? 

35.  A  mechanic  sold  a  carriage  for  15  dollars,  and 
a  sleigh  for  48  dollars  ;  what  did  he  receive  for  both  ? 


Id  INTELLECTUAL   ARITHMETIC.  [8* 

36.  A  soldier  was  33  years  of  age  when  he  en- 
gaged in  the  battle  of  New  Orleans ;  what  was  his 
age  44  years  after  ? 

37.  A  farmer  received  29  dollars  for  some  pork, 
18  dollars  for  some  hay,  15  dollars  for  some  oats,  and 
12  dollars  for  four  cords  of  wood ;  how  many  dollars 
did  he  receive  for  the  whole  ? 

38.  Thomas  hoed  13  rows  of  corn,  Lyman  16  rows, 
Cyrus  14  rows,  and  Warren  10  rows;  how  many 
rows  did  they  all  hoe  ? 

39.  A  gentleman  gave  30  dollars  for  a  coat,  7 
dollars  for  a  vest,  11  dollars  for  a  pair  of  pantaloons, 
and  5  dollars  for  a  hat ;  what  was  the  cost  of  all  ? 

40.  Paid  60  dollars  for  a  carriage,  which,  with  25 
dollars,  I  gave  for  a  horse ;  paid  12  dollars  for  his 
keeping,  and  then  sold  him  for  20  dollars  more  than 
he  cost  me  ;  for  how  much  did  I  sell  him  ? 

41.  A  man  deposited  40  dollars  in  a  bank,  which 
was  15  dollars  less  than  his  neighbor  deposited  at 
the  same  time  ;  how  much  did  both  deposit  ? 


CHAPTER  II. 

SUBTKACTION. 

8.     1.   James,  having  5  cents,  gave  2  cents  for  a 
pencil ;  how  many  cents  had  he  left  ? 

Analysis.  S'mce  James  had  5  cents^  and  gave  2  cents 
for  a  pencil^  he  had  left  the  difference  between  5  cents 
and  2  cents.  The  difference  hetioeen  5  cents  and  2  cents^ 
is  3  cents.      Therefore^  he  had  3  cents  left. 

2.  Mary  had  3  peaches,  and  ate  1  of  them ;  how 
many  had  she  left  ? 

3.  Ella  had  6  pinks,  and  gave  her  sister  2 ;  how 
many  had  she  left  ? 


8.j  INTELLECTUAL    ARITHMETIC .  17 

4.  On  a  rose  bush  were  7  roses,  and  Eliza  picked 
3  of  them  ;  how  many  were  left  ? 

5.  A  man  bought  10  sheep  and  sold  5  of  them ; 
how  many  had  he  left  ? 

6.  A  bad  boy  robbed  a  bird's  nest  of  7  eggs,  and 
broke  4  of  them  ;  how  many  remained  unbroken  ? 

7.  If  there  are  8  pigs  in  a  pen,  and  five  of  them 
get  out,  how  many  remain  ? 

8.  If  a  merchant  have  12  barrels  of  flour,  and 
be  sell  7  of  them,  how  many  barrels  will  he  have 
left  ? 

9.  Margaret  is  11  years  old,  and  Julia  4  years 
younger  ;  what  is  Julia's  age  ? 

10.  Steplien  had  9  marbles,  and  lost  3  of  them  ; 
how  many  had  he  left  ? 

11.  A  man,  earning  10  dollars  a  week,  spends  6 
dollars  for  i^rovisions;  how  many  dollars  has  he 
left? 

12.  Giles  borrowed  12  dollars,  and  paid  7  dollars 
of  it;  how  much  of  it  remained  unpaid  ? 

are  how  many? 
are  how  many  ? 
are  how  many  ? 
are  how  many? 
are  how  many  ? 
are  how  many? 
are  how  many? 
are  how  many? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 


13. 

5 

less 

3 

14. 

9 

less 

2 

15. 

7 

less 

4 

16. 

11 

less 

3 

17. 

8 

'.ess 

2 

18. 

6 

less 

4 

19. 

10 

less 

6 

20. 

7 

^.ess 

5 

21. 

14 

less 

8 

22. 

12 

less 

7 

23. 

9 

less 

8 

24. 

15 

less 

9 

25. 

20 

less 

6 

26. 

23 

less 

10 

27. 

18 

2 

less 

4 

18  INTELLECTUAL  ARITHMETIC.  [9. 

28.  11     from     14     leaves  bow  many  ? 

29.  9     from     12     leaves  Low  many  ? 

30.  7     from     16     leaves  how  many? 

31.  12     from     20     leaves  how  many  ? 

32.  10     from     IT     leaves  how  many? 

33.  8     from     18     leaves  how  many? 

34.  6     from     15     leaves  how  many? 

35.  11     from     21     leaves  how  many  ? 

36.  Take     5  from  12,  and  how  many  remain  ? 

37.  Take  10  from  19,  and  how  many  remain  ? 

38.  Take     7  from  11,  and  how  many  remain? 

39.  Take     9  from  13,  and  how  many  remain? 

40.  Take  12  from  23,  and  how  many  remain? 

41.  What  is  the  difference  between  14  and     6  ? 

42.  What  is  the  difference  between  20  and     8? 

43.  What  is  the  difference  between  19  and  15  ? 

44.  What  is  the  difference  between  11  and  22  ? 

45.  What  is  the  difference  between  17  and     6? 

46.  What  is  the  difference  between  25  and     9  ? 


O.  Subtraction  is  the  process  of  finding  the  difference 
between  two  numbers  ;  the  result  is  called  the  Difference  or 
Remainder.  The  sign  of  subtraction  is  written  thus,  — , 
and  is  read  minus.  Placed  between  two  numbers,  or  quan- 
tities, it  shows  that  the  one  after  it  is  to  be  taken  from  the 
one  before  it.  9  —  5  shows  that  5  is  to  be  subtracted  from 
S,  and  is  read  nine  minus  fi.ve. 

1.  How  many  are  10  —  6  ? 

2.  How  many  are     9  —  4  ? 

3.  How  many  are  12  —  7  ? 

4.  How  many  are  15  —  9  ? 

5.  How  many  are  20  —  8  ? 

6.  How  many  are  18  —  5  ? 

7.  How  many  are  17  —  3  ? 

8.  How  many  are  21  —  9  ? 


10.]  INTELLECTUAL   ARITHMETIC.  19 

9.  How  many  are  16  —     7  ? 

10.  How  many  are  19  —     9  ? 

11.  How  many  are  21  —  12? 

12.  How  many  are  17  —  10  ? 

13.  How  many  are  18  —     9  ? 

14.  How  many  are  20  —  11  ? 

15.  How  many  are  25  —  10  ? 

16.  How  many  are  32  —  12  ? 

17.  How  many  are  46  —  10? 

18.  How  many  are  57  —  34  ? 

Analysis.  57  is  equal  to  5  tens  and  7  units,  and  34  is 
equal  to  3  tens  and  4  units  ;  3  tens  from  5  tens  leave  2  tens, 
or  20,  and  4  units  from  7  units  leave  3  units,  which  added 
to  20  make  23.     Therefore,  57  —  34  =  23. 

19.  39  —  27  are  how  many  ? 

20.  43  —  32  are  how  many  ? 

21.  29  —  17  are  how  many  ? 

22.  54  —  21  are  how  many  ? 

23.  67  —  45  are  how  many  ? 

24.  75  —  25  are  how  many  ? 

25.  89  —  74  are  liow  vnany  ? 

26.  39  —  19  are  how  many  ? 

27.  41  —  30  are  how  many  ? 

28.  96  —  81  are  how  many? 


10.  1.  If  you  have  12  turkeys,  and  sell  9  of 
them,  liow  many  will  you  have  left  ? 

2.  A  grocer  had  10  boxes  of  lemons,  and  sold  6 
boxes  ;  how  many  boxes  had  he  left  ? 

3.  There  are  20  men  and  8  boys  at  work  in  a 
bookbindery ;  how  many  more  men  than  boys  are 
xhere  ? 

4.  From  a  cistern  holding  36  barrels  of  water,  12 
barrels  leaked  out ;  how  many  barrels  remained  ? 


20  INTELLECTUAL   ARITHMETIC.  [ 

5.  A  mail,  having  25  dollars  due  him,  received  a 
ton  of  hay  worth  11  dollars,  and  the  remainder  in. 
money  ;  how  much  money  did  he  receive  ? 

6.  There  are  46  .trees  in  an  orchard  ;  35  of  them 
are  apple  trees  and  the  remainder  peach  trees ;  how 
many  are  peach  trees  ? 

7.  From  a  piece  of  broadcloth  containing  27  yards, 
15  yards  were  cut ;  how  many  yards  remahied  ? 

8.  A  jeweler  bought  a  watch  for  60  dollars,  and 
sold  it  again  for  75  dollars :  how  much  did  he 
gain  ? 

9.  The  whole  number  of  pupils  registered  in  a 
certain  school  is  87,  and  but  Qo  are  in  attendance ; 
how  many  are  absent  ? 

10.  Charles  has  48  cents,  and  buys  a  slate  for  16 
cents  ;  liow  many  cents  has  lie  left  ? 

11.  There  are  36  wild  ducks  in  a  flock,  and  a 
huntsman  fires  at  them  and  kills  13 ;  how  many  are 
left? 

12.  A  farmer  sold  a  cow  for  22  dollars  that  cost 
him  30  dollars ;  how  much  did  he  lose  by  the  bar- 
gain ? 

13.  A  grocer  bought  a  quantity  of  sugar  for  39 
dollars,  and  sold  it  for  50  dollars  ;  how  much  did  he 
gain  ? 

14.  In  a  school  are  27  boys  and  35  girls ;  how 
many  more  girls  than  boys  ? 

15.  The  distance  from  Cincinnati  to  Miamisburg 
by  railroad  is  49  miles,  and  to  Dayton  60  miles ; 
wliat  is  the  distance  from  Miamisburg  to  Dayton  ? 

16.  In  a  warm  day  the  thermometer  indicated  85 
degrees ;  how  many  degrees  was  that  above  the 
freezing  point,  which  is  32  degrees  ? 

17.  A  man  died  at  the  age  of  77  years,  having 
been  married  49  years ;  what  was  his  age  when  he 
married  ? 


II.]  INTELLECTUAL   ARITHMETIC.  21 

II.    1.  4  and    7  and    9,  less    8,  are  how  many  ? 

2.  9  and  12  and    6,  less    7,  are  how  many  ? 

3.  14  and  10  and  12,  less  24,  are  how  many  ? 

4.  20  and  16  and    5,  less  14,  are  liow  many  ? 
6.   44  and  20  and  10,  less  50,  are  how  many  ? 

6.  27  and  15  and  12,  less  30,  are  how  many  ? 

7.  How  many  are    9  +  12  +  15  —  25  ? 

8.  How  many  are  26  +  15  +  7  —  18  ? 
■    9.   How  many  are  40  +  10  +  8  —  20  ? 

10.  How  much  less  than    64,  is  25  +  20  ? 

11.  How  much  less  than    5Q,  is  28  -f  16  ? 

12.  How  much  less  than  100,  is  46  +  34  ? 

13.  How  many  are  16  +  12  +  9  -}-  5  —  32 
+  8? 

14.  How  many  are  33  +  28  -f    9  —  30  ^h  15  ? 

15.  How  many  are  84  +  26  +  15  —  70  +  25  ? 

16.  A  man,  having  30  dollars,  paid  15  dollars  for 
a  coat,  5  dollars  for  a  vest,  and  4  dollars  for  a  hat ; 
how  much  had  he  left  ? 

Analysis.  He  had  left  the  diffei-ence  between  SO  dollars 
and  the  sum  of  \b  -\-  6  -\-  4  dollars;  15  dollars  and  5 
dollars  are  20  dollars,  and  4  dollars  are  24  dollars,  and  30 
dollars  less  24  dollars  are  6  dollars.      Therefore,  8^c, 

17.  Ellen  had  15  pinks,  and  she  gave  6  to  Mary 
and  4  to  Jane  ;  how  manv  had  she  left  ? 

18.  A  woman,  having  25  pounds  of  butter,  sold  15 
pounds  at  one  time,  and  10  pounds  at  another ;  how 
many  pounds  had  she  left  ? 

19.  Amasa  has  45  cents  in  three  boxes ;  in  the 
first  are  15  cents,  in  the  second  19  cents ;  how  many 
cents  are  in  the  third  box  ? 

20.  A  boy  found  8  apples  under  one  tree,  10  under 
another,  and  6  under  another ;  he  ate  3,  gave  away 
7,  and  carried  the  remainder  home;  how  many  did 
he  tak^  home  ? 


L 


22  INTELLECTUAL   ARITHMETIC.  [II. 

21.  Martin,  having  27  marbles,  gave  12  to  Albert, 
and  lost  5  ;  how  many  had  he  left  V 

22.  Reuben  had  16  cents ;  Charles  gave  him  10, 
Elisha  gave  him  9,  and  Henry  gave  him  enough  to 
make  his  number  42 ;  how  many  cents  did  Henry 
give  him  ? 

23.  A  merchant  bought  a  hogshead  of  sugar  for 
50  dollars  ;  he  paid  6  dollars  for  freight  and  customs, 
and  sold  the  whole  for  T5  dollars ;  how  much  did  he 
gain  ? 

24.  A  man  bought  a  watch  for  40  dollars,  a  chain 
for  15  dollars,  and  a  key  for  3  dollars,  and  he  sold 
the  whole  for  50  dollars  ;  how  much  did  he  lose  by 
the  bargain  ? 

25.  fSarah  bought  a  comb  for  12  cents,  some  rib- 
bon for  16  cents,  a  thimble  for  10  cents,  and  some 
thread  for  6  cents ;  how  much  had  she  left  of  fifty 
cents,  after  paying  for  these  articles  ? 

26.  A  drover  bought  9  sheep  of  one  man,  12  of 
another,  and  15  of  another  ;  he  afterwards  sold  8 
and  butchered  5  ;  how  many  had  he  left  ? 

27.  From  a  piece  of  calico  containing  26  yards 
Jane  bought  a  dress  of  9  yards,  and  Josephine  an- 
other of  10  yards  ;  how  many  yards  were  left  in  the 
piece  ? 

28.  Richard,  receiving  45  dollars  for  labor,  paid 
20  dollars  for  a  cow,  7  dollars  for  a  barrel  of  flour, 
and  9  dollars  for  three  cords  of  wood;  how  many 
dollars  had  he  left  ? 

29.  Four  men  bought  a  horse  for  80  dollars  ;  the 
first  gave  25  dollars,  the  second  20  dollars,  and  the 
third  18  dollars  ;  how  much  did  the  fourth  give  ? 

30.  A  boy  had  12  marbles  ;  another  boy  gave  him 
10  more,  another  9,  and  another  enough  more  to 
make  his  number  40  ;  how  many  did  the  last  boy 
give  him  ? 


11.]         •  INTELLECTUAL  ARITHMETIC.  23 

31.  A  man  traveled  22  miles  one  day,  and  26 
miles  the  second  day,  and  on  the  third  day  he  trav- 
eled 30  miles  on  his  return ;  how  many  miles  was  he 
from  the  place  from  which  he  first  started  ? 

32.  George  sold  two  dozen  eggs  for  20  cents,  one 
bushel  of  apples  for  37  cents,  and  received  a  pair  of 
skates  worth  75  cents  ;  how  much  did  he  still  owe 
for  his  skates  ? 

33.  A  man  owed  his  grocer  18  dollars,  his  tailor 
20  dollars,  iShd  a  merchant  25  dollars ;  he  paid  the 
grocer  10  dollars,  the  tailor  12  dollars,  and  the 
merchant  15  dollars  ;  how  much  did  he  still  owe 
them  all  ? 

34.  Bought  a  horse  for  90  dollars,  a  cutter  for  40 
dollars,  and  a  harness  for  20  dollars,  and  then  sold 
the  whole  for  50  dollars  more  than  the  horse  cost 
me ;  did  I  gain  or  lose  by  the  bargain,  and  how 
much  ? 

35.  A  lady  bought  a  new  bonnet  for  7  dollars,  a 
dress  for  12  dollars,  a  pair  of  shoes  for  2  dollars,  and 
a  parasol  for  3  dollars ;  she  gave  the  merchant  3 
ten  dollar  bills ;  how  many  dollars  must  be  re- 
turned ? 

36.  A  tailor  bought  a  piece  of  cloth  containing  31 
yards,  from  which  he  sold  13  yards  to  one  man,  and 
11  yards  to  another ;  how  many  yards  were  left  of 
the  piece  ? 

37.  A  farmer  had  45  sheep  in  one  lot,  37  in  an- 
other, and  30  in  another  ;  from  the  first  he  sold 
20,  from  the  second  15,  and  from  the  third  12  ;  how 
many  had  he  at  first,  and  how  many  had  he  left? 

38.  A  person,  sitting  down  to  play,  counted  his 
money,  and  found  that  he  had  1  twenty  dollar  bill,  5 
ten  dollar  bills,  and  3  five  dollar  bills  ;  when  he  got 
up  from  play,  he  had  7  ten  dollar  bills  and  6  five  dol- 
lar bills  ;  did  he  gain  or  lose,  and  how  much  ? 


24 


INTELLECTUAL   ARITHMETIC. 


[13. 


13. 

2  times 
2  times 
2  times 
2  times 
2  times 
2  times 


CHAPTER  III. 
MULTIPLICATION. 


1  are  how  many  ?  2  t 

2  are  how  many  ?  2 


are  how  many  ? 

4  are  how  many  ? 

5  are  liow  many  ? 

6  are  how  many  ? 


2  t 

2  t 
2  t 

2t 


3  times  1 
3  times  2 
3  times  3 
3  times  4 
3  times  5 

3  ■  times  6 

4  times  1 
4  times  2 
4  times  3 
4  times  4 
4  times  5 
4  times  6 


are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 


3 
3 

o 
O 

3 
3 
3 


are  how  many  ?j  4  t: 
are  how  many  ?  j  4  t 
are  how  many  ?, 4  t 
are  how  many  ?j4  t 
are  how  many  ? ;  4 
are  how  many  ?  1 4 


mes  7  are  how  many  ? 
mes  8  are  how  many  ? 
mes  9  are  how  many  ? 
mes  10  are  how  many  ? 
mes  11  are  how  many  r 
mes  12  are  how  many  ? 

mes  7  are  how  many  ? 
mes  8  are  how  many  ? 
mes  9  are  how  many  ? 
mes  10  are  how  many  ? 
mes  11  are  hovy  many  ? 
mes  12  are  how  many  ? 

mes  7  are  how  many  ? 
mes  8  are  how  many  ? 
mes  9  are  how  many  ? 
mes  10  are  how  many  ? 
mes  11  are  how  many  ? 
mes  12  are  how  many  ? 


1.  How  many  are  2  times  6  ?  2  times  8  ?  2 
times  7  ?     2   times  11  ?     2  times  9  ?     2  times  12  ? 

2.  How  many  are  3  times  5  ?  3  times  10  ?  3 
times  9  ?     3  times  7  ?     3  times  6  ?     3  times  12  ? 

3.  How  many  are  4  times  4  ?  4  times  7  ?  4 
times  9  ?     4  times  6  ?     4  times  10  ?     4  times  8  ? 

4.  At  9  dollars  a  ton,  what  will  3  tons  of  hay  cost  ? 

Analysis.  Si7ice  one  ton  costs  9  dollars^  3  to7is^  icJiich 
are  3  times  1  ton^  lolll  cost  3  times  9  dollars  ;  3  times  9 
dollars  are  27  dollm^s.  Therefore^  at  9  dollars  a  ion^ 
S  ^o;r5  ^  Aa?/  «^?^7^  co5^  27  dollars. 


13.] 


INTELLECTUAL   ARITHMETIC. 


25 


5.  At  8  cents  a  quart,  what  will  4  quarts  of  blue- 
berries cost  ? 

6.  If  you  answer  11  questions  at  each  recitation, 
how  many  questions  would  you  answer  at  3  recita- 
tions ?  at  4  ? 

7.  What  will  4  pairs  of  shoes  cost  at  12  shillings 
a  pair  ? 

8.  If  a  ream  of  paper  cost  3  dollars,  what  will  2 
reams  cost  ?  3  reams  ?  4  reams  ? 

9.  Eight  New  York  shillings  make  a  dollar  ;  how 
many  shillings  in  3  dollars  ?  in  4  dollars  ?  in  5 
dollars  ? 

10.  At  12  cents  a  yard,  what  will  3  yards  of  calico 
cost  ?  4  yards  ? 


AS. 

5  times 
times 
times 
times 
times 
times 


5 
5 
5 
5 
6 


5 
5 
5 
5 


6  times  1 
6  times  2 
6  times  3 
6  times  4 
6  times  5 

6  times  6 

7  times  1 
7  times  2 
7  times  3 
7  times  4 
7  times  5 
7  times  6 


1  are  how  many  ? 

2  are  how  many  ? 

3  are  how  many  ?  ^ 

4  are  how  many  ?  5 

5  are  how  many  ?  1 5 

6  are  how  many  ?  [  5 

are  how  many  ?'6 
are  how  many  ?  6 
are  how  many  ?  6 


are  how  many  ?  6 
are  how  many  ?'6 
ar~  ^ "^  '^ 


re  now  iiiciiiy  :  'u 
L'e  how  many  ?  1 6 


are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 
are  how  many  ? 


times  7  are  how  many  ? 
times  8  are  how  many  ? 
times  9  are  how  many  ? 
times  10  are  how  many  ? 
times  11  are  how  many? 
times  12  are  how  many  ? 

times  7  are  how  many? 
times  8  are  how  many  ? 
times  9  are  how  many  ? 
times  10  are  how  many? 
times  11  arc  how  many  ? 
times  12  are  how  many  ? 

times  7  are  how  many  ? 
times  8  are  how  many  ? 
times  9  are  how  many  ? 
times  10  are  how  many  ? 
times  11  are  how  many  ? 
times  12  are  how  many  ? 


26  INTELLECTUAL   ARITHMETIC.  [14. 

1.  How  many  are  5  times  6t   5  times  8  ?  5  times 

4  ?  5  times  3  ?  5  times  7  ?  5  times  12  ?  5  times  9  ? 

5  times  11? 

2.  How  many  are  6  times  3  ?  6  times  10  ?  6  times 

6  ?  6  times  9  ?  6  times  7  ?  6  times  11  ?  6  times  8  ? 

6  times  12  ? 

3.  How  many  are  7  times  2  ?  7  times  7  ?  7  times 
4  ?  7  times  9  ?  7  times  12  ?  7  times  10  ?  7  times  8  ? 

7  times  11  ?  7  times  6  ? 

4.  If  you  recite  8  perfect  lessons  in  1  week,  how 
many  would  you  recite  in  5  weeks  ?  in  6  weeks  ?  in 
7  weeks  ? 

5.  What  will  6  pounds  of  sugar  cost  at  10  cents  a 
pound  ?  at  9  cents  ? 

6.  If  you  write  5  lines  a  day,  how  many  lines  will 
you  write  in  4  days  ?  in  7  days  ? 

7.  What  cost  5  yards  of  ribbon,  at  8  cents  a  yard  ? 
at  9  cents  ? 

8.  AVliat  cost  7  barrels  of  apples  at  2  dollars  a 
barrel  ? 

9.  At  12  dollars  a  ton,  what  will  6  tons  of  hay 
cost  ?  7  tons  ?  5  tons  ? 

10.  If  a  boat  sail  9  miles  an  hour,  how  far  will 
she  sail  in  4  hours  ?  in  6  hours  ?  in  7  hours  ? 

11.  What  cost  7  barrels  of  flour,  at  11  dollars  a 
barrel  ? 

12.  There  are  7  days  in  1  week  ;  how  many  days 
in  5  weeks  ?  in  6  weeks  ?  in  9  weeks  ? 

1 


J&      JO.   ■ 

8  times  1  are  how  many  ?  1 8  times    7  are  how  many  ? 
8  times  2  are  how  many  ?  8  times    8  are  how  many  ? 


8  times  3  are  how  many  ? 
8  times  4  arc  how  many  ? 
8  times  5  arc  how  many  ? 


o   iiuitis  c>  circ  iiuw  many  :  o  innes  ii  are  now  many  ; 
8  times  6  are  how  many  ?  ^  8  times  12  are  how  many  ? 


8  times  9  are  how  many  ? 
8  times  10  are  how  many  ? 
8  times  11  are  how  many  ? 


14.]  INTELLECTUAL   ARITHMETIC.  27 

9  times  1  are  how  many  ?    9  times    7  are  how  many  ? 
9  times  2  are  how  many  ?    9  times    8  are  how  many  ? 

9  times    9  are  how  many  ? 

9  times  10  are  how  many  ? 

9  times  11  are  how  many  ? 

9  times  12  are  how  many  ? 


9  times  3  are  how  many  t 
9  times  4  are  how  many  ? 
9  times  5  are  how  many  ? 
9  times  6  are  how  many  ? 


10  times  1  are  how  many  ?  10  times    7  are  how  many  ? 
10  times  2  are  how  many  ?  10  times    8  are  how  many  ? 


10  times  3  are  how  many  ? 
10  times  4  are  liow  many  ? 
10  times  5  are  how  many  ? 
10  times  6  are  how  many  ? 


10  times  9  are  liow  many  ? 
10  times  10  are  how  many  ? 
10  times  11  are  how  many  ? 
10  times  12  are  how  many  ? 


1.  How  many  are  8  times  6  ?  8  times  4  ?  8  times 
9  ?  8  times  5  ?  8  times  10  ?     8  times  7  ?  8  times  11  ? 

8  times  8  ?  8  times  12  ? 

2.  How  many  are  9  times  3  ?  9  times  7  ?  9  times 
4  ?  9  times  6  ?  9  times  8  ?  9  times  12  ?  9  times  9  ? 

9  times  5  ?  9  times  11  ?  9  times  10  ? 

3.  How  many  are  10  times  10  ?  10  times  8  ?  10 
times  4  ?  10  times  7  ?  10  times  11  ? 

4.  What  will  8  barrels  of  flour  cost,  at  9  dollars  a 
barrel  ? 

5.  What  will  9  chairs  cost,  at  10  shillings  apiece  ? 

6.  If  5  boys  can  sit  on  one  bench,  how  many  can 
sit  on  7  benches  ?  on  8  benches  ? 

7.  If  Harvey  can  earn  10  dollars,  in  one  month, 
how  many  dollars  can  he  earn  in  8  months  ?  in  9 
months  ?  in  7  months  ? 

8.  If  8  men  can  do  a  piece  of  work  in  7  days,  how 
many  days  will  it  take  one  man  to  do  it  ? 

9.  If  two  barrels  of  flour  last  8  persons  3  months, 
how  lon^'  will  they  last  one  person  ? 

10.  How  many  dollars  will  buy  10  tons  of  hay,  at 
12  dollars  a  ton  ? 


28  INTELLECTUAL   ARITHMETIC.  [1*5. 

11.  A  farmer  divided  his  farm  into  9  fields,  con- 
taining 11  acres  each ;  how  many  acres  in  his 
farm  ? 

12.  If  a  man  travel  6  miles  an  hour,  how  far  will 
he  travel  in  7  hours  ?  in  8  hours  ?  in  9  hours  ?  in  6 
hours  ? 

13.  When  eggs  are  11  cents  a  dozen,  what  will  be 
the  cost  of  7  dozen  ?  of  9  dozen  ?  of  10  dozen  ? 


1*5.  • 

11  times  1  are  how  many  ? 
11  times  2  are  how  many  ? 
11  times  3  are  how  many  ? 
11  times  4  are  how  many  ? 
11  times  5  are  how  many  ? 
11  times  6  are  how  many  ? 


11  times  7  are  how  many  ? 
11  times  8  are  how  many  ? 
11  times  9  are  how  many  ? 
11  times  10  are  how  many  ? 
11  times  11  are  how  many  ? 
11  times  12  are  how  many  ? 


12  times  1  are  how  many  ?  12  times    7  are  how  many  ? 


12  times  2  are  how  many  ? 


12  times    8  are  how  many  ? 


12  times  3  are  how  many  ?  j  12  times  9  are  how  many  ? 
12  times  4  are  how  many  ? ,  12  times  10  are  how  many  ? 
12  times  5  are  how  many  ?  1 12  times  11  are  how  many  ? 
12  times  6  are  how  many  ?  \  12  times  12  are  how  many  ? 

1.  How  many  are  11  times  6  ?  11  times  10  ?  11 
times  7  ?  11  times  12  ?  11  times  8  ?     11  times  11  ? 

11  times  5  ? 

2.  How  many  are  12  times  10  ?  12  times  9  ?  12 
times  7  ?  12  times  8  ?  12  times  6  ?     12  times  11  ? 

12  times  5  ?  12  times  12  ? 

3.  What  will  be  the  cost  of  11  bunches  of  grapes, 
at  10  cents  a  bunch  ? 

4.  What  will  be  the  cost  of  12  barrels  of  pork,  at 
11  dollars  a  barrel  ? 

5.  What  will  11  yards  of  cloth  cost,  at  6  dollars  a 
yard  ? 


4 


1«5,]  INTELLECTUAL   ARITHMETIC.  29 

6.  In  an  orchard  are  12  rows  of  trees,  and  11 
trees  in  each  row  ;  how  many  trees  in  the  orchard  ? 

7.  What  will  11  turkeys  cost  at  6  dimes  apiece  ? 
at  7  dimes  ? 

8.  At  12  dollars  a  hundred,  what  will  7  hundred 
oak  posts  cost  ?     9  hundred  ?     11  hundred  ? 

9.  At  9  dollars  a  week,  what  will  5  weeks'  board 
cost  ?     8  weeks'  ?     11  weeks'  ?     12  weeks'  ? 

10.  If  the  fare  for  one  person  from  Albany  to  Bos- 
ton is  ^5  dollars,  what  will  be  the  fare  for  6  persons  ? 
for  9  persons  ?  for  12  persons  ? 

11.  At  12  dollars  a  month,  how  many  dollars  can 
a  man  earn  in  4  months  ?  in  6  months  ?  in  9 
months  ?  in  12  months  ? 

12.  If  it  take  9  yards  of  calico  for  one  dress,  how 
many  yards  will  be  required  to  make  4  dresses  ?  7 
dresses  ? 

13.  If  a  farmer  put  his  oats  into  7  bins,  each 
containing  12  bushels,  how  many  bushels  has  he  ? 

14.  If  I  put  8  dolkxrs  in  the  savings  bank  every 
month,  how  many  dollars  will  I  deposit  in  7  months  ? 
in  8  months  ?  in  12  months  ? 

15.  What  will  11  dozen  of  eggs  cost,  at  9  cents 
a  dozen  ?  at  10  cents  ?  at  11  cents  ? 

16.  If  a  quantity  of  provision  will  last  9  men  12 
days,  how  long  will  the  same  provision  last  one  man  ? 

17.  When  flour  is  7  dollars  a  barrel,  what  must 
be  paid  for  7  barrels  ?  for  8  barrels  ?  for  9  barrels  ? 
for  11  barrels  ? 

18.  If  12  bushels  of  apples  be  picked  from  each 
of  11  trees,  how  many  bushels  will  be  picked  from 

R  @»  Multiplication  is  the  process  of  finding  a  number  which  shall 
contain  one  of  two  given  numbers  as  many  times  as  there  are  units  in 
the  other ;   the  result  is  called  the  Product. 


30 


INTELLECTUAL   ARITHMETIC. 


[16. 


The  sign  of  multiplication  is  written  thus,  X,  and,  placed 
between  two  numbers  or  quantities,  shows  that  they  are  to 
be  multiplied  together.  5  X  4  =r  20,  shows  that  5  multi- 
plied  by  4  is  equal  to  20.  The  sign  is  commonly  called 
tiiiies,     5  X  4  is  read  5  times  4. 


1.  5x3  are  how  many  ? 

2.  7x4  are  how  many  ? 

3.  10  X  T  are  how  many  ? 

4.  3x8  are  how  many  ? 

5.  7x9  are  how  many  ? 

6.  12  X  6  are  how  many  ? 

7.  9x8  are  how  many  ? 


8.  8  X 11  are  how  many  ? 

9.  6x9  are  how  many  ? 

10.  5x    7  are  how  many  ? 

11.  11  xlO  are  how  many  ? 

12.  8x   4  are  how  many? 

13.  11x11  are  how  many  ? 

14.  12x12  are  how  many? 


15.  What  is  the  product  of  7  X  6  ?  of  9  X  5  ? 
of  7  X  7  ?  of  11  X  6  ? 

16.  What  is  the  product  of  4x3x2?  of  5x 
2  X  3?  of  3  X  3  x9? 

17.  What  will  be  the  cost  of  3  cows,  at  23  dollars 
apiece  ? 

Analysis.  Since  1  cow  cost  23  dollars,  3  coivsj  ivJach 
are  3  times  1  cow,  will  cost  3  times  23  dollars.  23  is  equal 
to  2  tens  and  3  units  ;  3  times  3  units  are  9  units,  and  3 
times  2  tens  are  6  tens,  or  60 ;  QO  and  ^  areQ%.  Therefore^ 
if  1  cow  cost  23  dollars,  3  cows  will  cost  69  dollars, 

18.  At  31  cents  a  bushel,  what  will  be  the  cost  of 
6  bushels  of  oats  ? 

19.  What  will  be  the  cost  of  7  bushels  of  apples, 
at  25  cents  a  bushel  ? 

20.  If  a  man  travel  26  miles  in  one  day,  how  far 
can  he  travel  in  10  days  ? 

21.  Mary  bought  6  yards  of  muslin  at  18  cents  a 
yard  ;  what  was  the  cost  of  the  whole  ? 

22.  Ephraim  is  17  years  old,  and  his  father  is  4 
times  as  old  ;  how  old  is  his  father  ? 


16.]  INTELLECTUAL   ARITHMETIC.  31 

23.  At  50  dollars  a  share,  what  will  7  shares  of 
bank  stock  cost  ? 

24.  What  will  9  pounds  of  tea  cost,  at  56  cents  a 
pound  ? 

25.  At  44  cents  a  day,  what  will  10  days'  labor 
amount  to  ? 

26.  At  3  dollars  a  yard,  what  wdll  be  the  cost  of  a 
piece  of  cloth  containing  36  yards  ? 

27.  What  will  be  the  cost  of  12  pounds  of  coffee, 
at  15  cents  a  pound  ? 

28.  If  the  cars  run  24  miles  an  hour,  how  far  will 
they  run  in  7  hours  ? 

29.  In  an  orchard  are  16  peach  trees,  and  6  times 
as  many  apple  trees ;  how  many  apple  trees  in  the 
orchard  ? 

30.  What  will  be  the  cost  of  45  lemons,  at  5  cents 
apiece  ? 

31.  If  11  men  can  do  a  piece  of  work  in  13  days, 
in  what  time  will  one  man  do  the  same  work  ? 

32.  If  a  man  labor  12  months  for  17  dollars  a 
month,  how  much  will  his  wages  amount  to  ? 

33.  At  3  dollars  a  barrel,  what  will  be  the  cost  oi 
28  barrels  of  potatoes  ? 

34.  If  in  an  orchard  are  12  rows  of  trees,  and 
32  trees  in  each  row,  how  many  trees  in  the  or- 
chard ? 

35.  If  a  man  can  dig  28  bushels  of  potatoes  in  one 
day,  how  many  bushels  can  he  dig  in  3  days  ?  in  4 
days  ?  in  5  days  ? 

36.  At  80  dollars  apiece,  what  will  be  the  cost  of 
3  horses  ?  of  4  horses  ?  of  6  horses  ? 

37.  At  43  dollars  an  acre,  what  will  10  acres  of 
land  cost  ?     12  acres  ? 

38.  If  8  horses  eat  3  bushels  of  oats  in  one  day, 
how  many  bushels  will  they  eat  in  7  days  ?  in  9 
days  ? 


g2  INTELLECTUAL   AEITHMETIC.  [17. 

17.  1.  What  will  be  the  cost  of  6  tons  of  coal, 
at  5  dollars  a  ton,  and  of  4  cords  of  wood  at  3  dol- 
lars a  cord  ? 

Analysts.  They  luill  cost  the  sum  of  the  products  of 
6X5  dollars,  and  o/  4  X  3  dollars  ;  6  times  5  dollars  are 
30  dollars,  and  4  times  3  dollars  are  1 2  dollars ;  30  dollars 
ojid  12  dollars  are  42  dollars.     Titer ef or e,  ^c. 

2.  A  farmer  sold  12  sheep  at  4  dollars  a  head, 
and  9  lambs  at  2  dollars  each ;  how  many  dollars 
did  he  receive  for  all  ? 

3.  What  will  be  the  cost  of  5  pounds  of  coffee  at 
15  cents  a  pound,  and  14  pounds  of  rice  at  6  cents  a 
pound  ? 

4.  If  two  persons  start  from  the  same  point,  and 
travel  in  opposite  directions,  one  at  the  rate  of  6 
miles  an  hour,  and  the  other  4  miles  an  hour,  how 
far  apart  will  they  be  in  7  hours  ?  in  9  hours  ?  in  12 
hours  ? 

5.  If  they  travel  in  the  same  direction,  how  far 
apart  will  they  be  in  5  hours  ?  in  7  hours  ?  in  24 
hours  ? 

6.  If  I  hire  a  man  and  his  son  to  labor,  the  father 
at  14  shillings  a  day,  and  the  son  at  8  shillings,  how 
much  will  be  due  them  both  in  6  days  ?  in  9  days  ? 

7.  Asa  has  16  marbles,  and  Omar  3  times  as 
many  ;  how  many  have  both  ? 

8.  A  drover  bought  28  sheep  at  3  dollars  a  head, 
and  5  cows  at  26  dollars  apiece ;  what  was  the  cost 
of  the  whole  ? 

9.  Justin  bought  9  oranges  at  4  cents  apiece,  7 
lemons  at  3  cents  apiece,  and  10  lead  pencils  at  2 
cents  apiece  ;  how  much  was  the  cost  of  the  whole  ? 

10.  Charles  is  twice  as  old  as  Byron,  and  Byron  is 
14  years  old ;  what  is  the  sum  of  their  ages  ? 

11.  In  a  8chool-room  16  pujoils  can  sit  on  each 


18.]  INTELLECTUAL   ARITHMETIC  83 

of  5  seats,  8  on  each  of  3  seats,  and  20  on  the  re- 
mainder of  the  seats ;  how  many  pupils  can  be  seat- 
ed in  the  room  ? 

12.  A  farmer  has  30  sheep  in  each  of  3  pastures, 
35  in  each  of  2  pastures,  and  40  in  another  pas- 
ture ;  how  many  sheep  has  he  in  all  ? 

13.  If  one  boy  earns  12  cents  a  day,  another  15 
cents  a  day,  and  another  20  cents  a  day,  how  much 
can  the  3  boys  earn  in  5  days  ? 

14.  A  man  bought  9  yards  of  cloth  for  a  suit  of 
clothes,  at  5  dollars  a  yard ;  he  paid  7  dollars  for 
making  the  coat,  2  dollars  for  making  the  pantaloons, 
and  1  dollar  for  making  the  vest ;  what  did  his  suit 
coet  him  ? 


18.  1.  A  farmer  bought  a  horse  for  85  dollars, 
for  which  he  gave  7  tons  of  hay  at  9  dollars  a  ton, 
and  the  remainder  in  money  ;  how  much  money  did 
he  pay  ? 

Analysis.  He  paid  in  money,  the  difference  between 
85  dollars  and  the  product  of  7  times  9  dollars  ;  7  times  9 
dollars  are  63  dollars,  and  85  dollars  less  63  dollars  are  22 
dollars.      Tfierefore,  SfC. 

2.  John  worked  5  days  for  15  cents  a  day,  and 
Norman  worked  4  days  for  20  cents  a  day  ;  how 
much  more  did  Norman  earn  than  John  ? 

3.  A  drover  bought  35  sheep  at  2  dollars  a  head, 
and  sold  them  for  90  dollars  ;  how  much  did  he  gain  ? 

4.  A  mechanic  earned  32  dollars  a  month  for 
five  months,  and  his  apprentice  12  dollars  a  month 
for  the  same  time  ;  how  much  more  did  the  one  earn 
than  the  other  ? 

5.  If  a  man  earn  90  cents  a  day,  and  pay  40  cents 
a  day  for  his  board,  how  much  will  he  save  in  6  days  ? 


84  INTELLECTUAL   ARITHMETIC.  [18. 

6.  A  farmer  sold  a  grocer  7  pounds  of  butter  at 
20  cents  a  pound,  and  received  in  payment  12  pounds 
of  fish  at  6  cents  a  pound ;  how  much  was  still  due 
the  farmer  ? 

7  c  !P-OW  much  difference  does  Mr.  Jones  receive, 
by  exchanging  5  cows  at  18  dollars  a  head,  for  1 
head  of  yovmg  cattle,  at  9  dollars  each  ? 

8.  A  merchant  poured  into  a  cask  14  quarts  of 
camphene  3  different  times,  and  from  the  same  cask 
filled  2  cans,  holding  8  quarts  each,  and  3  jugs,  hold- 
ing 6  quarts  each ;  how  many  quarts  remained  in 
the  cask  ? 

9.  Nellie  picked  6  quarts  of  blackberries,  and 
Laura  picked  4  times  as  many,  wanting  5  quarts  ; 
how  many  quarts  did  Laura  pick  ? 

10.  What  is  the  difference  in  the  cost  of  30  yards 
of  cloth  at  4  dimes  a  yard,  and  25  yards  at  3  dimes 
a  yard  ? 

11.  A  lady  bought  6  yards  of  satin,  at  2  dollars  a 
yard,  2  shawls  at  9  dollars  each,  and  some  lace  for  3 
dollars ;  she  paid  4  ten  dollar  bills  ;  how  much  ought 
she  to  receive  back  ? 

12.  A  drover  bought  50  sheep  for  125  dollars  ;  he 
sold  30  at  4  dollars  a  head,  and  the  remainder  at 
3  dollars  a  head ;  how  many  dollars  did  he  gain  by 
the  bargain  ? 

13.  Three  boys  talking  of  their  money,  one  said 
he  had  35  cents,  another  said  he  had  twice  as  many, 
and  the  third  said  he  had  as  many  as  both  the  others, 
wanting  10  cents  ;  how  many  cents  had  the  last  ? 

14.  Two  men  bought  a  horse  for  75  dollars  ;  they 
paid  2  dollars  a  week  for  keeping  liim,  and  at  the 
end  of  12  weeks  sold  him  for  90  dollars ;  how  much 
did  they  lose  by  their  bargain  ? 

15.  A  man,  owing  100  dollars,  gave  a  sleigh  worth 
40  dollars,  12  cords  of  wood,  at  3  dollars  a  cord, 


.]  INTELLECTUAL   ARITHMETIC.  i35 

and  the  remainder  in  money ;  Iioav  miicli  money  did 

he  pay  ? 

16.  I  bought  a  book-case  for  28  dollars,  a  table 
for  14  dollars,  and  6  chairs  at  2  dollars  each ;  I  paid 
for  the  table  ;  how  much  did  I  still  owe  ? 

17.  If  a  blacksmith  earn  11  shillings  a  day,  and  a 
joiner  11  shilHngs  a  day,  what  will  the  difierence  in 
their  earnings  amount  to  in  12  days  ? 

18.  Perry  paid  3  cents  for  a  lemon,  Elisha  twice 
as  much  for  a  pineapple,  and  for  a  melon  Albert  paid 
6  tunes  as  much,  lacking  15  cents,  as  was  paid  for 
both  the  lemon  and  the  pineapple ;  what  would  be 
the  cost  of  3  melons  at  the  same  rate  ? 

19.  At  a  public  meeting  are  35  gentlemen,  and 
8  times  as  many  ladies  lacking  30  ;  how  many  ladies 
are  there,  and  how  many  ladies  and  gentlemen  ? 

20.  Peter  has  4  times  5  peaches,  and  Marcus  has 
3  times  6  ;  how  many  will  they  both  have  left  after 
Peter  gives  away  7,  and  Marcus  5  ? 

21.  How  many  are  4  times  20,  plus  3  times  10  ? 

22.  How  many  are  7  times  15,  plus  9  times  12  ? 

23.  How  many  are  12  times  11,  minus  10  times  7  ? 

24.  How  many  are  10  times  11,  less  15,  plus  6 
times  5  ? 

25.  How  much  less  is  7  times  14,  than  3  times  40  ? 

26.  How  much  less  is  10  times  10,  than  6  times 
20  plus  25  ? 

27.  How  much  more  is  8  times  16,  than  7  times 
13   minus  11  ? 

28.  How  many  are  9  times  12,  plus  22  -f-  10  —  30  ? 

29.  How  many  are  15  X  12,  -f-  20  X  5  ? 

30.  How  manv  are  40  X  4,  +  27  X  3  ? 

31.  How  many  are  16  X  9,  —  13  X  6  ? 

32.  How  many  are  10  +  12,  X  6,  —  40  ? 

38.    How  many  are  14  X  8,  +  18,  +  12,  --^  7  ? 


36  INTELLECTUAL   ARITHMETIC.  [19. 

CHAPTER   lY. 

DIVISION. 

19.  1.  When  wheat  is  2  dollars  a  bushel,  how 
many  bushels  can  be  bought  for  12  dollars  ? 

Analysis.  Since  2  dollars  ivill  buy  1  bushel^  12  <:?o/- 
Zars  ■^^^7/  t>wy  «5  many  bushels  as  2  dollars,  the  price  of  1 
bushel,  is  contained  times  in  12  dollars  j  '2  dollars  is 
contained  in  12  dollars  G  times.  Therefore,  at  2  dollars 
a  bushel,  G  bushels  of 'tcheat  can  be  bought  for  12  dollars, 

2.  How  many  peaches  at  2  cents  apiece,  can  be 
bought  for  18  cents  ? 

3.  If  you  can  buy  one  lead  pencil  for  3  cents,  how 
many  can  you  buy  for  24  cents  ? 

4.  For  16  dollars,  how  many  cords  of  wood  can 
be  bought  at  4  dollars  a  cord  ? 

5.  At  3  cents  apiece,  how  many  oranges  can  be 
bought  for  21  cents  ? 

6.  In  how  many  days  can  a  man  earn  20  dollars, 
if  he  earn  2  dollars  a  day  ? 

7.  Edward  has  15  peaches,  which  he  wishes  to  di- 
vide equally  among  his  3  brothers  ;  how  many  must 
lie  give  to  each  ? 

8.  How  many  times  2  in  8  ?  in  6  ?  in  10  ?  in  14  ? 
in  16  ?  in  20  ?  in  24  ? 

9.  How  many  times  3  in  6  ?  in  12  ?  in  18  ?  in 
21  ?  in  9  ?  in  27  ?  in  33  ?  in  24  ?  in  36  ? 

10.  How  many  times  4  in  12  ?  in  8  ?  in  16  ?  in 
20  ?  in  36  ?  in  24  ?  in  40  ?  in  32  ?  in  48  ? 

11.  How  many  tons  of  coal,  at  4  dollars  a  ton, 
can  be  bought  for  48  dollars  ? 

12.  If  one  penholder  can  be  bought  for  4  cents, 
how  many  can  be  bought  for  20  cents  ?  for  32  cents  ? 
for  40  cents  ? 


so.]  INTELLECTUAL   ARITHMETIC.  87 

13.  Paid  36  dollars  for  3  gold  cliaiiis ;  what  was 
the  cost  of  each  ? 

14.  How  many  barrels  of  apples,  at  3  dollars  a 
barrel,  can  be  bought  for  36  dollars  ? 

15.  If  you  give  41  cents  to  4  beggars,  how  many 
do  you  give  to  each  ? 

16.  If  a  man  Avalk  3  miles  an  hour,  how  many 
hours  will  it  take  him  to  walk  30  miles  ? 

17.  Bought  4  barrels  of  flour  for  28  dollars  ;  what 
was  the  cost  of  one  barrel  ? 

18.  If  I  pay  27  cents  for  3  pounds  of  sugar,  how 
much  do  I  pay  a  pound  ? 

19.  15  are  how  many  times  3  ?  5  ? 

20.  36  are  how  many  times  3  ?  6  ?  4  ? 

21.  42  are  how  many  times  6  ?  7  ?  3  ? 

22.  24  are  how  many  times  2  ?  6  ?  4  ?  8  ? 

23.  16  are  how  many  times  4  ?  2  ?  8  ? 

24.  40  are  how  many  times  8  ?  5  ?  4  ? 

25.  72  are  how  many  times  8  ?  6  ?  12  ? 

26.  56  are  how  many  times  7  ?  8  ?  4  ? 

27.  48  are  how  many  times  4  ?  6  ?  8  ?  12  ? 

28.  32  are  how  many  times  8  ?  2  ?  4  ? 

29.  30  are  how  many  times  5  ?  6  ?  3  ? 


SO.  1.  How  many  spools  of  thread,  at  5  cents  a 
spool,  can  be  bought  for  40  cents  ?  for  50  cents  ? 

2.  When  lard  is  7  cents  a  pound,  how  many 
pounds  can  be  bought  for  56  cents  ?  for  63  cents  ? 

3.  If  a  farmer  divide  84  bushels  of  potatoes 
equally  among  7  laborers,  how  many  bushels  will 
each  receive  ? 

4.  If  an  orchard  contain  64  trees,  and  8  trees  in  a 
row,  how  many  rows  are  there  ? 

5.  If  a  man  travel  72  miles  in  6  hours,  how  far 
does  he  travel  in  one  hour  ? 


38  INTELLECTUAL    ARITHMETIC.  [!^0. 

6.  Levi  paid  7  cents  for  liis  ball ;  how  many  balls 
at  the  same  price  could  he  buy  for  28  cents  ?  for 
56  cents  ?  for  6S  cents  ?  for  84  cents  ?  • 

7.  How  many  bins  will  be  required  to  hold  72 
bushels  of  wheat,  if  each  bin  contain  8  bushels  ? 

8.  At  5  dollars  a  week,  how  long  will  it  take  a 
man  to  earn  45  dollars  ?  50  dollars  ? 

9.  At  8  cents  a  pound,  how  many  pounds  of 
su2:ar  can  be  bouorht  for  96  cents  ? 

10.  If  a  man  spend  6  cents  a  day  for  cigars,  how 
many  days  will  60  cents  last  him  ? 

11.  A  man  bought  some  sheep  for  48  dollars,  at 
4  dollars  apiece  ;  how  many  sheep  did  he  buy  ? 

12.  If  one  man  can  do  a  job  of  work  in  60  days, 
in  what  time  can  5  men  do  tlie  same  Avork  ? 

13.  45  are  how  many  times  5  ?  9  ?  3  ? 

14.  36  are  how  many  times  4  ?  6  ?  9  ?  12  ? 

15.  80  are  how  many  times  10  ?  8  ?  4  ?  5  ? 

16.  96  are  how  many  times  8  ?  6  ?  12  ?  4  ? 

17.  44  are  how  many  times  11  ?  4  ?  2  ? 

18.  24  are  how  many  times  2  ?  8  ?  4  ?  6  ?  12  ? 

19.  60  are  how  many  times  6  ?  5  ?  10  ?  12  ? 

20.  63  are  how  many  times  9  ?  3  ?  7  ? 

21.  84  are  how  many  times  7?  12?  4?  6? 

22.  90  are  how  many  times  9  ?  6  ?  10  ? 

23.  108  are  how  many  times  12  ?  9  ?  6  ? 

24.  100  are  how  many  times  10  ?  20  ?  5  ? 

25.  99  are  how  many  times  9  ?  11  ?  3  ? 

26.  81  are  how  many  times  9  ? 

27.  6Q  are  how  many  times  11  ?  6  ?  3  ? 

28.  75  are  how  many  times  15  ?  5  ?  25  ? 

29.  88  are  how  many  times  4  ?  11  ?  8  ? 

30.  120  are  how  many  times  12  ?  10  ?  8  ? 

31.  140  are  how  many  times  7  ?  10  ?  20  ? 

32.  200  are  how  many  times  20  ?  40  ?  50  ? 


SH.]  MTELLECTUAL   ARITHMETIC.  ,     39 

SI,  1.  If  6  men  receive  72  dollars  for  building 
a  barn,  how  many  dollars  will  each  man  receive  't 

Note.  If  the  pupil  is  sufficiently  acquainted  with  FractionSf 
the  iollowing  Analysis  is  often  prelerred.* 

ANALYSIS.  If  G  7nen  receive  *72  dollars,  1  man,  loMch 
is  J  o/Q  onen,  vnll  receive  J  of  72  dollars  ;  ^  of  72  dol- 
lars is  12  dollars.  Therefore  if  G  ^nen  receive  72  dol- 
lars for  building  a  barn,  each  man  will  receive  12  dollars, 

2.  If  81  cents  be  paid  for  9  dozen  of  eggs,  what 
will  be  the  cost  of  1  dozen  ? 

3.  A  mechanic  sold  a  wagon  for  77  dollars,  and 
took  his  pay  in  hay,  at  11  dollars  a  ton ;  how  many 
tons  did  he  receive  ? 

4.  How  long  will  it  take  12  men  to  perform  a 
piece  of  work  that  1  man  can  do  in  48  days  ? 

5.  Paid  108  dollars  for  9  thousand  feet  of  lum- 
ber ;  what  was  the  cost  of  a  thousand  feet  ? 

6.  How  many  barrels  of  flour  can  be  bought  for 
5G  dollars,  at  7  dollars  a  barrel  ?  at  8  dollars  ? 

7.  How  many  cows,  at  12  dollars  a  head,  can  be 
bought  for  60  dollars?  for  96  dollars?  for  120  dollars? 

8.  When  steak  is  10  cents  a  pound,  howluany 
pounds  can  be  bought  for  50  cents  ?  for  80  cents  ? 
for  100  cents  ? 

9.  At  11  cents  a  pound,  how  many  poimds  of 
sugar  can  be  bought  for  88  cents  ?  for  99  cents  ? 

*  When  it  is  necessary  to  express  a  qunntity  less  than  a  unit,  we  ma/ 
regard  the  unit  as  diviaed  into  some  number  of  equal  parts,  aud  ubo 
one  of  these  parts  as  a  new  unit  of  less  value  than  the  unit  divided. 
Thus,  if  a  yard  be  divided  into  two  equal  parts,  each  of  the  parts  is 
culled  one  half ;  -when  into  tliree  equal  parts,  each  of  the  parts  is  called 
one  tJurd  ;  "VVi.en  into  four  equal  parts,  each  of  the  parts  is  called  one 
fourth  ;  when  into^i'^  equal  parts,  each  of  the  parts  is  called  one-fifth  ; 
two  of  the  parts,  tuvjfths,  &c. ;  when  into  sic  equal  parts,  each  of  the 
parts  is  called  one  such  j  tivo  ox  the  parts,  tivo  sixths,  three  of  the  parts, 
tliree  sixths,  (tc. 


40  INTELLECTUAL   ARITHMETIC.  [31. 

10.  A  man  planted  an  orchard  of  132  trees,  and 
put  11  trees  in  a  row ;  how  many  rows  in  the  orchard  ? 

11.  A  farmer  sold  a  horse  for  120  dollars ;  how 
many  cows  at  12  dollars  each  would  pay  for  the 
horse  ?  How  many  young  cattle  at  8  dollars  each  ? 
How  many  sheep  at  5  dollars  each  ? 

12.  If  25  sheep  cost  75  dollars,  what  will  1  sheep 
cost  ? 

13.  If  a  boy  read  7  pages  a  day,  how  long  will  it 
take  him  to  read  56  pages  ?  to  read  84  pages  ?  98 
pages  ? 

14.  At  15  cents  a  pound,  how  many  pounds  of 
coftee  can  be  bought  for  45  cents  ?  for  60  cents  ?  for 
90  cents  ? 

15.  If  1  man  can  do  a  piece  of  work  in  72  days, 
m  what  time  can  6  men  do  it  ?  8  men  ?  9  men  ?  12 
men  ? 

16.  If  a  certain  quantity  of  provision  will  last  1 
man  36  days,  how  many  days  will  it  last  4  men  ?  9 
men  ?  12  men  ? 

17.  A  man  earns  66  dollars  in  11  weeks ;  how 
much  does  he  earn  in  1  week  ?  how  much  in  1  day  ? 

18.  ^  If  a  painter  receive  100  dollars  for  painting  5 
carriages,  how  much  does  he  receive  apiece  ? 

19.  How  many  lots  containing  12  acres  each  can 
be  sold  from  a  farm  of  120  acres  ?  how  many  lots  of 
20  acres  each  ? 

20.  If  a  steamboat  run  11  miles  an  hour,  how 
long  will  she  be  in  running  44  miles  ?  88  miles  ? 
110  miles  ? 

21.  How  many  men,  at  8  dollars  a  month,  can  be 
hired  one  month  for  96  dollars  ?  how  ma^iy  at  12 
dollars  ?  how  many  at  16  dollars  ? 

22.  If  I  travel  120  miles  in  6  days,  how  many 
iniles  do  I  travel  in  1  day  ? 


22.]  INTELLECTUAL   ARITHMETIC.  41 

22.  1.  If  3  pounds  of  coffee  cost  2T  cents,  wlmt 
"will  6  pounds  cost '? 

Analysis.  Jf  S  pounds  of  coffee  cost  27  cents,  1  pound, 
u-Jiich  is  1  third  of  3  pounds,  ivill  cost  1  ^/^/rc?  o/'  27  cents, 
cr  9  cen^s.  Jf  \  pound  cost  9  cents,  6  pounds,  which  are 
6  ^me5  1  pound,  will  cost  G  ^mes  9  ce?i^5,  or  54  ce?i('s. 
Therefore,  if  3  pounds  of  coffee  cost  27  ce?i^5,  G  pounds  will 
cost  54  ce7Z^5. 

Or  thus  :  Q  pounds  ivill  cost  G  tiines  1  third  of  21  cents;  1 

jf/i/rc?  ci/'27  ce?i^s  is  9  ce/^^5,  a;zc^  G  times  9  cew^s  are  54  cents. 

Therefore,  ^c. 

Or  0  pounds,  ivMch  are  2  ii?ne5  3  r>ound?,  will  c^st  2  times  27  cewi^?,  <ir. 

2.  If  4  yards  of  broadcloth  cost  20  dollars,  what 
Trill  9  yards  cost  ? 

3.  If  6  barrels  of  flour  cost  54  dollars,  what  will 
T  barrels  cost  ? 

4.  If  9  yards  of  ribbon  cost  72  cents,  what  will 
4  yards  cost  ? 

5.  If  a  man  travel  40  miles  in  8  hours,  how  far 
will  ho  travel  in  6  hours  ?  in  9  hours  ? 

6.  If  5  coats  can  bo  cut  from  20  yards  of  cloth, 
how  many  yards  would  be  required  to  cut  7  coats  ? 

7.  If  9  Aveeks'  board  cost  45  dollars,  what  will  4 
weeks'  board  cost  ?  7  weeks'  ?  12  weeks'  ? 

8.  If  a  boy  earn  60  cents  in  5  days,  how  many 
cents  will  he  earn  in  12  days  ?  in  20  days  ? 

9.  Yfhat  will  bo  the  cost  of  10  cords  of  wood,  if 
G  cords  cost  24  dollars  ? 

10.  What  will  be  the  cost  of  14  dozen  of  eggs,  if 
12  dozen  cost  120  cents  ? 

11.  If  18  apples  are  worth  6  peaches,  how  many 
apples  are  15  peaches  worth  ?  20  peaches  ? 

12.  If  a  stage  coach  run  48  miles  in  8  hours,  in 
how  many  hours  will  it  run  60  miles  ? 

13.  If  15  yards  of  cloth  cost  75  dollars,  what  will 
40  yards  cost  ? 

4* 


i2  INTELLECTUAL   ARITHMETIC.  [SS. 

14.  How  many  melons  can  be  bought  for  100 
^ents,  at  the  rate  of  3  for  60  cents  ? 

15.  What  will  42  pounds  of  beef  cost,  if  7  pounds 
cost  56  cents  ? 

16.  When  apples  are  sold  at  tlie  rate  of  4  barrels 
for  8  dollars,  how  many  barrels  must  be  given  for  3 
tons  of  coal  at  6  dollars  a  ton  ? 

17.  How  many  dozen  of  eggs,  at  12  cents  a  dozen, 
will  pay  for  15  pounds  of  sugar,  at  8  cents  a  pound  ? 

18.  Hovf  many  gallons  of  molasses,  at  50  cents  a 
gallon,  will  pay  for  20  pounds  of  lard,  worth  10  cents 
a  pound  ? 

19.  If  a  farmer  sell  5  firkins  of  butter,  worth  12 
dollars  a  firkin,  for  cloth  worth  4  dollars  a  yard,  how 
many  yards  will  he  receive  ? 

20.  If  5  barrels  of  cider  are  worth  15  dollars,  how 
many  hundred  weight  of  pork, worth  6  dollars  a  hun- 
dred weight,  would  8  barrels  of  cider  buy  ? 

21.  If  6  bushels  of  wheat  are  worth  12  dollars, 
how  many  bushels  of  wheat  must  be  given  for  9  tons 
of  hay,  worth  10  dollars  a  ton  ? 

22.  At  the  rate  of  3  for  4  cents,  how  many  pears 
can  be  bought  for  24  cents  ? 

Analysis.  Since  4  ce7its  icill  buy  3  pears^  24  ceyits  will 
buy  as  many  times  3  pears  as  4  cents  is  contained  times 
in  24  cents  •  4  cents  are  co7itained  in  24  ceiits  6  times^ 
and  6  times  3  are  IS  pears.  Therefore^  if  3  pears  can  be 
bought  for  4  cents^  18  2^ea7-s  7nay  be  bought  for  24  ceiits. 

23.  A  man  paid  72  cents  for  some  oranges,  at  the 
rate  of  5  for  12  cents  ;  how  many  oranges  did  he  buy? 

24.  How  many  pounds  of  nails  may  be  bought  for 
60  cents,  at  the  rate  of  4  pounds  for  20  cents  ? 

25.  When  eggs  are  sold  at  tlie  rate  of  9  for  11 
cents,  how  many  must  be  sold  to  receive  99  cents  ? 

26.  At  the  rate  of  16  miles  in  4  liours,  how  many 
miles  would  a  man  travel  in  12  hours  ? 


S3.]  INTELLECTUAL   ARITHMETIC.  43 

27.  If  3  men  can  do  a  piece  of  work  in  12  days, 
how  many  days  will  it  take  9  men  to  do  the  same  ? 

AxALYSis.  If  ^  men  can  clothe  icorh  in  12  days, 
1)  men  can  do  it  in  I  of  3  times  12  cicnjs  ;  3  ti7nes  12 
cknjs  are  36  ckiijs,  and  i  of  3Q  days  are  4  days.  There- 
fare,  <&c. 

28.  If  6  men  can  build  a  wall  in  8  days,  how 
many  men  will  be  required  to  build  it  in  3  days  ? 

29.  If  4  men  can  dig  a  ditch  in  10  days,  how 
many  days  will  it  take  1  man  to  dig  it  ?  5  men  ?  8 
men  ? 

30.  How  long  will  it  take  7  men  to  reap  a  field, 
if  it  take  14  men  2  days  to  reap  it  ? 

31.  If  5  men  can  build  a  barn  in  8  days,  how 
many  men  would  be  required  to  build  it  in  1  day  ? 
in  2  days  ?  in  4  days  ? 

32.  A  man  bought  some  oranges  for  44  cents,  at 
the  rate  of  5  for  11  cents,  and  divided  them  equally 
among  his  4  children ;  how  many  did  he  give  to 
each  ? 

33.  If  15  days'  work  will  pay  for  10  cords  of 
wood,  at  3  dollars  a  cord,  what  is  the  price  of  1 
day's  labor  ? 

34.  A  man  engaged  to  labor  5  months  for  80  dol- 
lars, but  by  request  continued  3  months  longer,  at 
the  same  rate ;  what  amount  will  be  due  him  for  the 
whole  time  ? 

35.  If  you  pay  60  cents  for  some  lemons,  at  the 
rate  of  6  for  10  cents,  and  sell  them  at  the  rate  of  9 
for  20  cents,  how  many  cents  will  you  gain  by  the 
operation  ? 

36.  If  two  ships  are  120  miles  apart,  and  sail 
directly  toward  each  otlier,  one  at  the  rate  of  9 
Kiiles  an  hour,  and  the  other  at  the  rate  of  11  miles 
an  hour,  how  many  hours  before  they  will  meet  ? 


44  INTELLECTUAL   ARITHMETIC.  [23. 


Division  is  the  process  of  finding  bow  many  times 
one  number  is  contained  in  another;  and  the  result  is  callec* 
the  Quotient.  The  sign  of  division  is  written  thus,  -^,  and, 
placed  between  two  numbers  or  quantities,  shows  that  the 
one  on  the  left  is  to  be  divided  by  the  one  on  the  right. 
24  -|-  8  =  3  shows  that  24  divided  by  8  is  equal  to  3. 

1.  How  many  times    9  are  6  times    6  ? 

2.  How  many  times    4  are  5  times    8  ? 

3.  How  many  times    8  are  6  times  12  ? 

4.  How  many  times  10  are  5  times  20  ? 

5.  How  many  times  15  are  3  times  25  ? 

6.  How  many  times  20  are  10  times  12  ? 

7.  How  many  times  16  are  8  times    8  ? 

8.  How  many  times  28  are  7  times  16  ? 

9.  How  many  times  25  are  5  times  30  ? 

10.  How  many  times  20  are  12  times  10  ? 

11.  16  times    4  are  how  many  times    8  ? 

12.  9  times  12  are  how  many  times    6  ? 

13.  8  times  14  are  how  many  times  16  ? 

14.  4  times  42  are  how  many  times  12  ? 

15.  7  times  18  are  how  many  times    9  ? 

16.  14  times  10  are  how  many  times  28  ? 

17.  12  times    8-1-4  are  how  many  times  10  ? 

18.  6  times  15  -j-  20  are  how  many  times  12  ?  * 

19.  How  many  times  9  +  3  are  7  times  13  less  10  ? 

20.  How  many  times  18  —  4  are  8  times  12  +  2  ? 

21.  In  8  X  12,  how  many  times  64  -^  8  ? 

22.  In  6  X  20  +  12,  how  many  times  55  4-  5  ? 

23.  In  48  -{-  24  divided  by  6,  how  many  times  4  ? 

24.  How  many  times  12  —  7  are  9  times  8  ? 

25.  How  many  times  9  +  6  in  6  times  12  +  3  ? 

26.  How  many  times  27  +  9  +   7  X  3  are  8  X 
11  +  20  ? 

*  Each  sign  affects  only  the  number  placed  after  it.     When  there  is  a 
remainder  in  the  result,  let  it  simply  be  mentioned  as  such. 


34.]  INTELLECTUAL   APvITHMETIC.  45 


.« 


94,  1.  How  many  vests,  at  5  dollars  eacli,  will 
pay  for  7  weeks'  board,  at  6  dollars  a  week,  and  18 
dollars  borrowed  money  ? 

2.  If  a  man  receive  16  pounds  of  sugar  in  ex- 
change for  20  pounds  of  cheese  at  8  cents  a  pound, 
■n^hat  is  the  price  of  the  sugar  per  pound  ? 

3.  James  paid  36  cents  for  some  oranges  at  3 
cents  apiece,  and,  after  eating  5  of  them,  lie  gave 
the  remainder,  at  4  cents  apiece,  for  a  knife  ;  how 
much  did  the  knife  cost  him  ? 

4.  Omar  bought  30  peaches  at  the  rate  of  2  for  3 
cents,  and,  after  eating  3  of  them  and  giving  3  to 
his  brother,  he  sold  the  remainder  at  the  rate  of  3 
for  7  cents  ;  did  he  gain  or  lose  by  the  bargain,  and 
how  mucli  ? 

5.  A  farmer  sold  9  sheep  at  12  shillings  a  head, 
and  11  bushels  of  oats  at  2  shillings  a  bushel ;  how 
many  yards  of  cloth,  at  10  shillings  a  yard,  will  pay 
the  deijt  ? 

6.  If  I  buv  40  turkevs  at  the  rate  of  5  for  3  dol- 
lars,  and  sell  them  at  the  rate  of  8  for  7  dollars,  how 
much  will  I  gain  by  the  operation  ? 

7.  If  a  drover  buy  24  lambs  for  30  dollars,  at  how 
much  must  he  sell  them  a  head  to  gain  18  dollars  on 
the  cost  ? 

8.  If  5  men  buy  a  mowing  machine  for  120  dol- 
lars, and  rent  it  3  weeks  for  15  dollars  a  week,  and 
then  sell  it  for  100  dollars,  what  is  each  man's  share 
of  the  o-ain  ? 

9.  If  5  barrels  of  flour  are  worth  30  dollars,  how 
many  yards  of  cloth  worth  3  dollars  a  yard  will  2 
barrels  of  the  flour  buy  ? 

10.  Four  men  agree  to  build  120  rods  of  wall  for 
48  dollars,  and  to  share  equally ;  but  when  the  wall 
is  half  built,  2  men  quit,  and  tlie  others  finish  it ; 
how  many  dollars  must  each  receive  ? 


46  INTELLECTUAL   ARITHIMETIC. 


11.  How  many  sheep  can  I  buy  for  75  dollars  at 
the  rate  of  3  for  7  dollars,  and  have  12  dollars  left  ? 

12.  A  man,  having  80  dollars,  bought  9  cords  of 
wood  at  4  dollars  a  cord,  3  barrels  of  flour  at  8  dol- 
lars a  barrel,  and  the  remainder  he  expended  for 
cloth  at  4  dollars  a  yard  ;  how  many  yards  of  cloth 
did  he  buy  ? 

13.  If  4  bushels  of  wheat  are  worth  12  bushels  of 
corn,  how  many  bushels  of  corn  are  equal  in  value 
to  10  bushels  of  wheat  ? 

14.  If  12  bushels  of  wheat  make  3  barrels  of  flour, 
how  many  bushels  of  wheat  will  make  7  barrels  ? 

15.  A  cistern  holding  140  gallons  has  a  pipe  by 
which  30  gallons  will  run  into  the  cistern  in  one 
hour,  and  another  that  will  discharge  20  gallons  in 
an  hour  ;  when  both  are  running,  in  what  time  will 
the  cistern  be  filled  ? 

16.  If  a  quantity  of  provision  serve  7  men  12 
days,  how  long  would  it  serve  4  men  ? 

17.  A  merchant  bought  15  bushels  of  clover  seed 
for  75  dollars  ;  ho  wishes  to  keep  3  bushels  for  his 
own  use,  and  to  sell  the  remainder  so  as  to  make  9 
dollars  on  the  first  cost  of  the  whole  ;  how  much 
must  he  ask  a  bushel  ? 

18.  A  man  bouglit  a  span  of  horses  for  80  dollars 
each  ;  he  spent  40  dollars  in  fitting  them  for  market, 
and  then  sold  them  for  oOO  dollars  ;  what  was  his 
gain  on  each  horse  ? 

19.  A  tailor  bought  15  yards  of  one  kind  of  cloth 
for  60  dollars,  and  25  yards  of  another  kind  for  75 
dollars  ;  Avhat  was  the  difference  in  the  price  per 
yard  ? 

20.  A  thief,  having  36  miles  the  start  of  an  officer, 
travels  at  the  rate  of  6  miles  an  hour  ;  the  oflicer 
pursues  at  the  rate  of  9  miles  an  hour  ;  in  how  many 
hours  will  he  overtake  the  thief? 


S4.]  INTELLECTUAL   ARITHMETIC.  47 

21.  Add  5  to  22,  divide  the  sum  by  9,  multiply 
the  quotient  by  12,  subtract  6  from  the  product,  and 
add  10  to  the  remainder  ;  what  will  be  the  result  ? 

22.  Divide  40  by  8,  multiply  the  quotient  by  9, 
to  the  product  add  11,  from  the  sum  take  6,  and 
what  will  remain  ? 

23.  Multiply  20  by  4,  subtract  40,  add  10,  divide 
by  5,  multiply  by  7,  and  what  is  the  result  ? 

24.  From  36  subtract  6,  divide  the  remainder  by 
5,  multiply  the  quotient  by  12,  add  15  to  the  product, 
subtract  77  from  the  sum,  divide  the  remainder  by 
10,  and  what  will  be  the  quotient  ? 

25.  Add  5  and  7  to  8,  multiply  the  sum  by  3, 
from  the  product  subtract  5,  divide  the  remainder 
by  11,  multiply  the  quotient  by  6,  add  20  to  the 
product,  and  what  will  be  the  sum  ? 

26.  Subtract  10  from  6  multiplied  by  8,  to  the 
remainder  add  4,  divide  the  sum  by  6,  multiply  the 
quotient  by  11,  subtract  7  from  the  product,  divide 
the  remainder  by  10,  add  30  to  the  quotient,  and 
what  will  be  the  sum  ? 

27.  Multiply  15  by  5,  add  5,  divide  by  8,  multiply 
by  6,  subtract  10,  divide  by  5,  add  2,  multiply  by  11, 
and  what  will  be  the  product  ? 

28.  10 +  8-^6x9  —  7x5  + 20 -MO +  8  = 
how  many  ? 

29.  8  X  9  -f-12  +  3  X  5  + 10  -Ml  X  8  +  20  — 
12  +  4  X  7  —  3  =  how  many  ? 

30.  25  —  5  ^  2  X  9  -h  10  -^-  20  X  12  +  15  —  5 
-i-  7  -[-  8  -f-  2  =  how  many  ? 

31.  36-^9x12  +  8^7x5+10  —  25-^-5  + 
4x9  —  ll-M0x6-^3  =  how  many  ? 

Note.  The  above  examples  will  afford  a  thorough  and  profitable 
mental  drill  to  the  pupil,  and  also  familiarize  the  signs  and  terms  used 
in  the  preceding  pages,  and  which  must  be  well  understood  in  the  com- 
meccement  of  the  study  of  Written  Arithmetic.  The  teacher  can  extend 
the  number  of  examples  at  pleasure. 


48  INTELLECTUAL   ARITHMETIC.  [25 • 

CHAPTER  Y. 
KEDUCTION. 

Table  of  United  States  Money. 


10  mills  (m.) 

make 

1  cent, 

c. 

10  cents 

u 

1  dime, 

d. 

10  dimes 

(( 

1  dollar, 

$. 

10  dollars 

a 

1  eagle, 

E. 

Note.    Dollars  and  cents  are  separated  by  a  period  (.) ;  thus,  $2.10,  is 
read  2  dollars  10  cents. 

A  Simple  Number  contains  but  one  name  or  denomina- 
tion ;  thus,  5,  84,  12  bushels,  Q>b  dollars,  are  simple  numbers. 

A  Compound  Number  contains  two  or  more  names  or 
denominations  ;  thus,  5  dollars  25  cents,  16  bushels  3  pecks, 
3  days  10  hours,  are  compound  numbers. 

Reduction  is  the  process  of  changing  numbers  from  one 
denomination  to  another,  without  altering  their  value  ;  thus, 
changing  pounds  to  ounces,  ounces  to  pounds,  dollars  to 
cents,  &c.,  is  reduction. 

1.  How  many  mills  in  2  cents?  in  8  cents? 

2.  How  many  cents  in  1  dime  ?  in  3  dimes  ? 

3.  How  many  dimes  in  8  dollars?  in  4  dollars? 

4.  How  many  dollars  in  2  eagles?  in  5  eagles? 

5.  How  many  cents  in  4  dimes  and  7  cents? 

6.  How  many  dimes  in  3  dollars  and  6  dimes? 

7.  If  Jamas  earned  12  dollars,  and  his  father  3 
eagles,  how  many  dollars  did  they  both  earn  ? 

8.  A  man  has  4  eagles,  4  five  dollar  bills,  and  4 
dimes  ;  how  many  dollars  and  cents  has  he  ? 

9.  How  many  dimes  are  equal  to  40  cents?  to  70 
cents  ? 

10.  What  is  the  diiference  in  the  cost  of  8  yards 
of  cloth  at  2  dimes  a  yard,  and  6  yards  at  30  cents  a 
yard  ? 


26,  27.]      intellectual  arithmetic.  49 

26.  Table  of  English  Money. 


4  farthings  (far.) 

make 

1  penny, 

d. 

12  pence 

(( 

1  shilling, 

s. 

20  shillings 

u 

1  pound, 

£, 

Note.    A  sovereign  (sov.)  is  equal  in  value  to  one  pound. 

1.  How  many  farthings  in  1  penny  ?  in  3  pence  ? 
in  6  pence  ?  in  9  pence  ? 

2.  How  many  pence  in  1  shilling  ?  in  4  shillings  ? 
in  5  shillings  ?  in  9  shillings  ?  in  10  shillings  ? 

3.  How  many  pence  in  8  farthings  ?  in  24  far- 
things ?  in  48  farthings  ? 

4.  How  many  shillings  in  24  pence  ?  in  84  pence  ? 
in  108  pence  ? 

5.  How  many  pounds  in  40  shillings  ?  in  120  shil- 
lings ? 

6.  At  5  shillings  a  yard,  how  many  pounds  will 
20  yards  of  carpeting  cost  ? 

7.  At  7  shillings  a  pair,  how  many  pairs  of  shoes 
can  be  bought  for  2  sovereigns  ? 


ST.  Table  of  Troy  Weight. 

24  grains  (gr.)       make     1  pennyweight,    pwt. 
20  pennyweights         "        1  ounce,  oz. 

12  ounces  "        1  pound,  lb. 

1.  How  many  grains  in  2  pennyweights  ?  in  4  ? 

2.  How  many  pennyweights  in  3  ounces  ?  in  5  ? 

3.  How  many  pennyweights  in  96  grains  ?  in  124 
grains  ? 

4.  In  120  pennyweights  how  many  ounces  ?  in 
200  pennyweights  ? 

5.  What  will  a  gold  chain,  weighing  15  penny- 
weights cost,  at  8  dimes  a  pennyweight  ?  how  many 
dollars  and  cents  ? 

4 


60  intellectual  arithmetic.  [28. 

38,  Table  of  Avoirdupois  Weight- 

16  drams  (dr.)  make  1  ounce,  oz. 

16  ounces  "  1  pound,  lb. 

100  pounds  "  1  hundred  weight,  cwt. 

20  hundred  weight       "  1  ton.  T. 

1.  How  many  drams  in  3  ounces  ?  in  4  ounces  ? 
in  6  ounces  ? 

2.  How  many  ounces  in  32  drams  ?  in  48  drams  ? 
in  64  drams  ? 

8.   How  many  ounces  in  3  pounds  ?  in  5  lbs.  ?  in 
7  lbs.  ? 

4.  How  many  ounces  in  2  lbs.   6  oz.  ?   in  4  lbs. 
10  oz.  ? 

5.  In  3  cwt.  and  5  lbs.,  how  many  pounds  ? 

6.  In  5  pounds,  how  many  ounces  ? 

7.  How  many  pounds  in  3  cwt.  ?   in  6  cwt.  ?  in 
9  cwt.  ? 

8.  In  16  tons,  how  many  cwt.  ?  in  25  tons  ? 

9.  In  1  ton  and  5  cwt.,  how  many  cwt.  ?    how 
many  pounds  ? 

10.  How  many  dollars  will  3  cwt.  of  flour  cost,  if 
25  pounds  cost  5  dimes  ? 

11.  What  will  1  ton  and  5  cwt.  of  hay  cost,  if  5 
cwt.  cost  3  dollars  ? 

12.  What  will  2  cwt.  10  lbs.  of  beef  cost  at  6  cents 
a  pound  ? 

13.  If  8  ounces  of  tea  cost  4  dimes,  what  will  2 
pounds  cost  ? 

14.  What  will  be  the  cost  of  4  cwt.  of  sugar,  at  7 
cents  a  pound  ? 

15.  Which  will  cost  the  more,  5  cwt.  of  fish  at  6 
cents  a  pound,  or  3  tons  of  \my  at  50  cents  a  cwt.  ? 

16.  What  will  1  ton  of   hay  cost  at  1  cent  a 
pound  ? 


29.]  intellectual  arithmetic.  61 

29.  Table  of  Long  Measure. 


12    inches  (in.)                mak( 

3 1  foot,         ft. 

3    feet 

1  yard,         yd. 

5^-  yards,  or  IG^-  feet,         " 

1  rod,          rd. 

40    rods                                " 

1  furlong,   fur. 

8    furlongs,  or  320  rods,    " 

1  mile,         mi. 

3    miles                               " 

1  leao'ue,     lea. 

O             7 

69i  miles                               " 

1  degree,     deg.  or  ^. 

860    deo-rees                          " 

1  circle  of  the  earth. 

1.  Ho^v  many  inches  in  3  ft.  ?  in  5  ft.  ?  in  10  ft.  ? 
in  12  ft.? 

2.  How  many  feet  in  4  yards  ?  in  6  yards  ?  in  9 
yards  ? 

3.  How  many  yards  in  15  feet  ?  in  24  feet  ? 

4.  How  many  yards  in  2  rods  ?  in  4  rods  ? 

5.  How  many  furlongs  in  5  miles  ?  in  7  miles  and 
4  furlongs  ? 

6.  How  many  furlongs  in  80  rods  ?  in  120  rods  ? 
in  160  rods  ? 

7.  In  2  miles  4  fur.  20  rods,  how  many  rods  ? 

8.  How  many  leagues  in  9  miles  ?  in  18  miles  ?  in 
36  miles  ? 

9.  How  many  inches  in  3  yds.  1  ft.  10  in.  ? 

10.  In  108  inches  how  many  yards  ?  in  144 
inches  ? 

11.  If  a  man  travel  5  miles  an  hour,  how  long 
will  it  take  him  to  travel  20  leagues  ? 

12.  If  a  ship  sail  20  leagues  a  day,  how  long  will 
it  take  her  to  sail  from  New  York  to  Liverpool,  it 
being  3000  miles  ? 

13.  In  100  inches  how  many  yards,  feet,  and 
inches  ? 

14.  At  8  dimes  a  foot,  how  many  dollars  will  3  yds. 
1  ft.  of  iron  railing  cost  ? 

15.  In  2  rods  5  feet,  how  many  inches  ? 


52  INTELLECTUAL   ARITHMETIC.         [SO,  31, 

SO.  Table  of  Cloth  Measure. 

2|  inches  (in.)       make     1  nail,  na. 

"^  ii3.ils  "       1  quarter  of  a  yard,  qr. 

4  quarters  "         1  yard,  yd. 

1.  How  many  nails  in  3  qrs.  ?  in  5  qrs.  ? 

2.  How  many  nails  in  2  yds.  2  qrs.  ? 

3.  How  many  quarters  in  5  yds.  ?    in  6  yds.  3 
qrs.  ? 

4.  How  many  yards  in  16  qrs.  ?  in  56  qrs.  ? 

5.  How  many  qrs.  in  36  nails  ?  in  64  na.  ? 

6.  How  many  qrs.  in  5  yds.  ?    in  6  yds.  ?    in  7 
yds.  ? 

7.  In  4  yards,  how  many  nails  ? 

8.  In  6  yards,  how  many  qrs.  ? 

9.  In  123  nails,  how  many  yards  ? 


9  square  feet 

30:^  square  yards 

40  square  rods 

4  roods 

640  acres 

US.       Table  of  Land  or  Square  iviiiASURE. 

144  square  inches  (sq.in.)  make  1  square  foot,  sq.  ft. 

1  square  yard,  sq.yd. 
1  square  rod,  P. 
1  rood,  R. 

1  acre,  A. 

1  square  mile,  Sq.  M. 

1.  How  many  square  feet  in  5  square  yards  ?    in 
10  square  yards  ?  in  20  square  yards  ? 

2.  How  many  square  yards  in  36  sq.  ft.  ?  in  72 
sq.  ft.  ?  in  108  sq.  ft.  ? 

3.  How  many  square  rods  in  3  roods  ?  in  5  roods  ? 
in  7  roods  ? 

4.  How  many  acres  in  20  roods  ?  in  80  roods  ? 

5.  At  4  dollars  a  square  rod,  what  would  2  roods 
10  rods  of  land  cost  ? 


33.  33.]         INTELLECTUAL   ARITHMETIC.  53 

3S.  Table  of  Cubic  Measure. 

1728  cubic  inches  (cu.  in.)  make  1  cubic  foot,  cu.  ft. 

27      "     feet  "     1  cubic  yard,  cu.  yd. 

24|    "     feet  "     1  perch  of  stone, Pch. 

16      "     feet  "     1  cord  foot,    c.  ft. 

8  cord  feet,  or  )  u     -\        ^    ?        An 

-ic^cy      ^^    V    \      \  1  cord 01  wood,  C. 

128  cubic  feet      )  ' 

1.  How  many  cubic  feet  in  2  cubic  yards  ?  in   3 
cubic  yards  ? 

2.  How  many  cubic  feet  in  2  perch  of  stone  ?  in 
4  perch  ?  in  6  perch  ? 

3.  How  many  cord  feet  in  3  cords  of  wood  ?  in  7 
cords  ?  in  9  cords  ? 

4.  How  many  cord  feet  in  120  cubic  feet  of  wood  ? 
in  200  cubic  feet  ? 

5.  How  many  cords  in  24  cord  feet  ?  in  b^  cord 
feet? 


^3.  Table  of  Liquid  Measure. 

4    gills  (gi.)  make  1  pint,  pt. 

2    pints  "  1  quart,  qt. 

4    quarts  "  1  gallon,  gal. 

31|-  gallons  "  •  1  barrel,  bar. 

2    barrels,  or  63  gallons  "  1  hogshead,  hhd. 

1.  How  many  gills  in  4  pints  ?  in  6  pints  ?  in  10 
pints  ? 

2.  How  many  pints  in  3  quarts  ?  in  8  quarts  ?  in 

1  gallon  ?  in  3  gallons  ? 

3.  How  many  gills  in  4  quarts  ?  in  6  quarts  ?  in 
8  quarts  ? 

4.  How  many  quarts  in  3  gallons?    how  many 
pints  ?   how  many  gills  in  3  quarts  ?  in  1  gallon  and 

2  quarts  ? 


54  INTELLECTUAL   ARITHMETIC.  [34, 

5.  How  many  gills  in  2  gallons  2  qts.  ? 

6.  How  many  quart  cups  could  be  filled  from  a 
10  gallon  keg  of  wine  ?  how  many  pint  bottles  ? 

7.  In  48  gills,  how  many  pints  ?  quarts  ? 

8.  How  many  gallons  in  64  gills  ?  in  96  gills  ? 

9.  How  many  quarts  in  56  pints  ?  gallons  ? 

10.  In  10  gallons,  how  many  quarts  ?  pints  ? 
gills  ? 

11.  What  will  be  the  cost  of  6  gallons  of  burning 
fluid,  at  15  cents  a  quart  ? 

12.  If  a  pint  of  molasses  cost  7  cents,  what  will  a 
gallon  cost  ? 

13.  If  one  gallon  of  oil  cost  90  cents,  what  will  3 
gallons  and  2  quarts  cost  ? 

14.  If  you  should  draw  10  gallons  and  3  quarts 
from  a  hogshead  of  molasses,  how  much  would  re- 
main ? 


Table  of  Dry  Measure. 

2  pints  (pt.)  make     1  quart,  qt. 

8  quarts  "         1  peck,  pk. 

4  pecks  "        1  Wshel  bu. 

1.  How  many  pints  in  1  peck  ?  in  2  pks.  4  qts.  ? 

2.  How  many  quarts  in  1  bu.  2  pks.  ? 

§.    In  2  bu.  1  pk.  6  qts.  how  many  quarts  ? 

4.  In  64  quarts  how  many  pecks  ?  bushels  ? 

5.  In  80  pints  how  many  pecks  ? 

6.  At  3  cents  a  pint,^  what  will  be  the  cost  of  one 
peck  of  chestnuts  ? 

7.  If  one  bushel  of  hickory  nuts  cost  160  cents, 
what  will  be  the  cost  of  6  quarts  ? 

8.  Bought  2  pecks  of  cranberries  for  96  cents,  and 
sold  them  for  5  cents  a  pint;  how  much  was  the 
gain  ? 


35.] 


INTELLECTUAL   ARITHMETIC. 


m 


35. 


Table  of  Time. 


60  seconds  (sec.)     make 
60  minutes 
24  hours 

7  days 
12  calendar  months 

365  days 

366  days 
100  years 


u 


ii 


a 


a 
ii. 
u 
u 


1  minute.  m. 

1  hour,  hr. 
1  day,                   '    d. 

1  week,  w. 

1  year,  yr. 
1  common  year,      yro 

1  leap  year,  yr. 

1  century,  C. 


The  divisions  of  the  year,  the  names  of  the  months, 
and  the  number  in  each,  are  shown  in  the  following 
table :  — 


Wnrf  Of 

(1st 
(  2d 

month, 

January       has    31  days 

Y  >  lliLt-'i  . 

a 

February        ' 

'      28*    " 

(3d 

a 

March             < 

'      31     '^ 

Spring. 

{4th 

a 

April               * 

'      30     " 

(5th 

a 

May                 * 

•'     31     " 

(6th 

ii 

Juno               * 

='      30     " 

Summer. 

^Tth 

ii 

July 

'.i       31       a 

(8th 

ii 

August 

u       31       a 

(  9th 

ii 

September 

'''      30     " 

Autumn. 

\  10th 

ii 

October 

u       31       a 

( 11th 

u 

^SJ^ovember 

^'      30     " 

Winter. 

12th 

u 

December 

u       31       u 

The  following  lines  will   help  to   remember  the 
number  of  days  in  each   month  :  — 

Tliirty  days  hath  September, 
April,  June,  and  November; 

All  the  rest  have  thirty -one, 

Save  February,  -which  alone 
Hath  twenty-eight;  and  one  day  more 
We  add  to 'it,  one  year  in  four. 


*  In  leep-year,  29. 


B6  INTELLECTUAL   ARITHMETIC.  [S6, 

1.  How  many  seconds  in  2  minutes  ?  in  5  minutes  ? 

2.  How   many    seconds   in    10   minutes  ?    in   20 
minutes  ? 

3.  How  many  seconds  in  1  hour  ?  in  2  hours  ? 

4.  How  many  minutes  in  3  hours  ?  in  5  hours  ? 

5.  How  many  liours  in  2  days  ?  in  3  days  ? 

6.  In  2  days  and  12  hours  how  many  hours  ? 

7.  In  6  weeks  how  many  days  ?  in  9  weeks  ? 

8.  How  many  weeks  in  49  days  ?  in  84  days  ? 

9.  How  many  weeks  and  days  in  75  days  V  in  90 
days  ? 

10.  How  many  hours  in  3  days  10  hours  ? 

11.  In  36  months  how  many  years  ?  in  84  months  ? 

12.  How  many  days  from  January  1st  to  March 
10  th,  inclusive  ? 

13.  How  many  days  from  April  10th  to  the  15th 
of  June  ? 


!6.              Miscellaneous  Table.. 

12  units                   mak 

e  1  dozen. 

12  dozen                      " 

1  gross. 

12  gross                        " 

1  great  gross. 

20  units                        " 

1  score. 

24  sheets  of  paper      " 

1  quire. 

20  quires                      " 

1  ream. 

5Q  pounds                    " 

1  bushel  of  corn. 

60  pounds                    " 

1  bushel  of  wheat. 

196  pounds                    " 

1  barrel  of  flour. 

200  pounds                   " 

J  1  barrel  of  beef,  pork, 
(      or  fish. 

1.  TVhat  cost  1  ream  of  paper,  at  20  cents  a  quire  ? 

2.  What  cost  3  dozen  lemons,  at  3  cents  apiece  ? 

3.  What  cost  2  gross  of  pens,  at  5  cents  a  dozen  ? 

4.  At  7  dollars  a  hundred  pounds,  what  will  2 
barrels  of  pork  cost  ? 


37.]  INTELLECTUAL   ARITHMETIC.  57 

CHAPTER  YI. 
FKACTIONS. 

S7o  1.  TVhat  is  understood  by  one  half,  one 
third,  one  fourth,  one  fifth,  &c.  ? 

Ans.  When  a  number  or  thing,  as  a  unit  or  an 
apple,  is  divided  into  two  equal  parts,  each  of  the 
parts  is  called  one  half;  when  into  three  equal  parts, 
each  of  the  parts  is  called  one  third ;  two  of  the  parts 
are  called  two  thirds^  <tc. 

2.    How  many  halves  in  1  ? 

8.   How  many  thirds  in  1  ? 

4.  If  a  peach  be  divided  into  2  equal  parts,  what 
is  each  part  called  ? 

5.  If  an  orange  be  divided  into  3  equal  parts, 
what  are  the  parts  called  ? 

6.  How  many  halves  in  4  ? 

ANALYSTS.  Since  in  1  there  are  2  halves,  in  4  there  are  4 
times  2  halves,  or  8  halves.  Therefore  there  are  8  halves  in  4. 

T.   How  many  halves  in  5  ?  in  6  ? 

8.  How  many  halves  in  7  ?  in  7  and  1  half? 

9.  How  many  thirds  in  3  ?  in  4  ?  in  5  ? 

10.  How  many  thirds  in  7  ?  in  8  ?  in  9  ? 

11.  How  many  thirds  in  6  and  1  third  ?  in  6  and 
2  thirds  ? 

12.  How  many  halves  in  5  ?  how  many  thirds  ? 

13.  How  many  halves  in  10  and  1  half  ? 

14.  How  many  thirds  in  9  and  2  thirds  ? 

15.  In  8  halves  how  many  whole  things  ? 

Analysis.  Since  in  2  hcdves  there  is  one  whole  thing, 
in  8  hcdves  there  are  as  many  whole  things  as  2,  the  num- 
ber of  halves  in  1,  is  contained  times  in  8,  tohich  is  4 
times,     Thercforc-i  in  8  halves  there,  are  4  lohole  things. 


58  ,  INTELLECTUAL   ARITHMETIC.  [37, 

16.  How  many  whole  things  m  12  halves  ?  in  16 
halves  ?  in  24  halves  ? 

17.  How  many  whole  things  in  9  thirds  ?  in  18 
thirds  ? 

18.  How  many  whole  things  in  10  halves  ?  in  12 
thirds  ?  in  21  thirds  ?  in  20  halves  ? 

19.  How  many  half  bushels  in  3  bushels  and  1 
half  ? 

20.  John  gave  6  peaches  to  his  2  brothers ;  what 
part  of  them  did  each  have  ? 

21.  What  is  1  half  of  6  ? 

A:n'alysis.  It  is  that  oiiimher  lohich  taken  2  times 
will  make  G ;  2  times  3  is  G.  Tha^efore  3  is  1  half 
o/G, 

22.  What  is  1  third  of  9  ?  of  18  ?  of  27  ?  of  36  ? 

23.  What  is  1  half  of  8  ?  of  12  ?  of  18  ?  of  22  ? 

24.  How  can  you  take  1  half  of  an  orange  ?  1  third  ? 

25.  How  can  you  take  2  thirds  of  an  apple  ? 

26.  William  had  30  new  pennies,  and  John  had 
1  half  as  many  ;  how  many  had  John  ? 

27.  If  a  pound  of  candles  cost  15  cents,  whaf  will 
1  third  of  a  pound  cost  ?  2  thirds  ? 

28.  George  is  12  years  old,  and  Mary  is  2  thirds 
as  old  as  he  ;  how  old  is  Mary  ? 

29.  If  a  barrel  of  flour  cost  10  dollars,  and  a 
barrel  of  cider  1  half  as  much,  what  is  the  cost  of 
the  cider  ? 

30.  If  3  tons  of  hay  cost  27  dollars,  what  part  of 
27  dollars  will  1  ton  cost  ?  2  tons  ? 

31.  A  boy,  having  33  cents,  spent  2  thirds  of  them ; 
how  many  had  he  left  ? 

32.  Edwin  gave  2  peaches  and  1  half  to  his  sister, 
and  1  peach  and  1  half  to  his  brother ;  how  many 
peaches  did  he  give  to  both  ? 

33.  A  farmer,  ha\ang  44  sheep,  sold  1  half  of  them ; 
how  many  had  he  left  f 


38.]  INTELLECTUAL   ARITHMETIC.  59 

3S.  1.  Wliat  do  you  understand  by  1  fourth? 
8  fourths  ? 

2.  Wliat  do  you  understand  by  1  fifth  ?  2  fifths  ? 
3  fifths  ?  4  fifths  ? 

3.  What  do  you  understand  by  1  sixth  ?  3  sixths? 
5  sixths  ? 

4.  How  can  you  take  1  fourth  of  any  thing  ?  1 
sixth  ? 

5.  How  can  you  take  3  fourths  of  any  thing  ?  3 
fifths  ? 

6.  How  many  fifths  in  1  ?  in  4  ?  in  6  ? 

7.  How  many  fourths  in  1  ?  in  2  and  3  fourths  ? 

8.  How  many  sixths  in  2  ?  in  3  and  4  sixths  ? 

9.  In  4  and  5  sixths  how  many  sixths  ? 

10.  In  8  and  3  fourths  how  many  fourths  ? 

11.  In  7  and  4  fifths  how  many  fifths  ? 

12.  Which  is  greater,  1  fourtli  or  1  fifth  ?  1  fifth 
or  1  sixth  ? 

13.  How  many  times  1  in  8  fourths  ?  in  16  fourths  ? 

14.  How  many  times  1  in  15  fifths  ?  in  25  fifths  ? 

15.  How  many  times  1  in  24  sixths  ?  in  36  sixtlis? 

16.  What  is  1  fourth  of  12  ?  of  20  ?  of  28  ? 

17.  What  is  1  sixth  of  18  ?  of  30  ?  of  42  ? 

18.  What  is  1  fourth  of  32  ?  of  40  ?  of  48  ? 

19.  What  is  1  fifth  of  10  ?  of  20  ?  of  50  ? 

20.  What  is  1  sixth  of  36  ?  2  sixths  ?  5  sixths  ? 

21.  What  is  1  fifth  of  40  ?  3  fifths  ?  4  fifths  ? 

22.  What  is  3  fourths  of  16  ?  of  24  ? 

23.  What  is  2  fifths  of  10  ?  of  25  ? 

24.  What  is  3  sixths  of  30  ?  5  sixths  of  42  ? 

25.  If  a  ton  of  hay  cost  12  dollars,  what  will  1 
taartli  of  a  ton  cost  ?  2  fourths  ?  3  fourths  ? 

23.  If  5  bushels  of  apples  cost  90  cents,  what  part 
of  90  cents  will  1  bushel  cost  ?  2  bushels  ?  3  bushels  ? 

27.  When  coal  is  6  dollars  a  ton,  what  part  of  a 
ton  can  be  bought  for  1  dollar  ?  for  2  dollars  ?  for  5 
dollars  ? 


60  INTELLECTUAL   ARITHMETIC.  [S8. 

28.  Bought  a  piece  of  land  for  45  dollars ;  what 
is  1  fifth  of  it  worth  ?  2  fifths  ?  3  fifths  ? 

29.  If  you  pay  30  dollars  for  one  month's  labor, 
what  do  you  pay  for  1  fifth  of  a  month  ?  for  1  sixth  ? 
for  5  sixths  ?  for  4  fifths  ? 

30.  A  man  divided  48  cents  equally  among  6 
beggars ;  what  part  of  the  whole  did  each  beggar 
receive  ?  what  part  did  2  receive  ?  3  ?  4  ?  5  ? 

31.  If  in  a  basket  of  54  eggs  1  sixth  are  bad,  how 
many  are  good  ? 

32.  If  a  man  earn  15  dollars  a  week,  and   spend 

2  fifths  of  it,  how  much  does  he  save  ? 

33.  A  drover,  having  60  sheep,  sold  1  fourth  of 
them  at  one  time,  and  1  fifth  at  another ;  how  many 
had  he  left  ? 

34.  Rollin  had  18  marbles,  and  gave  2  sixths  of 
them  to  Martin ;  now  many  did  he  give  Martin,  and 
how  many  did  he  keep  for  himself  ? 

35.  If  Harry  bought  6  pounds  of  coffee  for  1  dol- 
lar, what  part  of  1  dollar  did  1  pound  cost  ?  2  pounds  ? 

3  pounds  ?  4  pounds  ? 

36.  When  tea  is  5  shillings  a  pound,  what  part  of 
a  pound  can  be  bought  for  1  shilling  ?  2  shillings  ? 
3  shillings  ?  4  shillings  ? 

37.  If  a  barrel  of  pork  cost  15  dollars,  what  will 
2  thirds  of  it  cost  ?  3  fifths  ? 

38.  A  gentleman  is  60  years  old,  and  his  wife  is  4 
fifths  as  old  ;  how  old  is  she  ? 

39.  Andrew  is  18  years  old,  and  his  sister,  Jane,  is 
5  sixths  as  old  ;  how  old  is  Jane  ? 

40.  Paid  36  dollars  for  1  acre  of  land  ;  what  is  1 
sixtli  of  it  worth  ?  3  sixths  ?  1  fourth  ?  3  fourths  ? 

41.  If  you  divide  a  barrel  of  flour  equally  among 
5  poor  families,  v/hat  part  of  tlie  barrel  will  1  family 
receive  ?  2  families  ?  3  families  ?  4  families  ?  5  fam- 
ilies ? 


S9,]  INTELLECTUAL   ARITHMETIC.  61 

SO.     1.    What  do  you  understand  by  1  seventh  ? 

3  sevenths  ?  4  sevenths  ?  5  sevenths  ? 

2.  What  is  meant  by  1  eighth  ?  5  eighths  ?  1 
ninth  ?  3  ninths  ?  5  ninths  ?  7  ninths  ? 

3.  What  is  meant  by  3  tenths?  9  tenths?  5 
twelftlis  ?  11  twentieths  ? 

4.  How  many  ninths  in  a  unit,  or  whole  thing  ? 
how  many  tenths  ?  how  many  elevenths  ?  how  many 
twelfths  ?  how  many  twentieths  ? 

5.  How  many  times  1  in  14  sevenths  ?  in  32 
eigiiths  ?  in  45  ninths  ? 

G.  How  many  times  1  in  70  tenths  ?  in  44  elevenths  ? 
in  30  fifteenths  ?  in  80  twentieths  ? 

7.  ^Vhat  is  1  seventh  of  42  ?  of  63  ?  of  84  ? 

8.  What  is  1  eighth  of  24  ?  of  56  ?  of  64  ? 

9.  What  is  1  ninth  of  36  ?  3  ninths  ?  7  ninths  ? 

10.  What  are  3  tenths  of  50  ?  of  60  ?  of  90  ? 

11.  What  is  1  twelfth  of  72  ?  5  twelfths  ?  7  twelfths  ? 

12.  What  is  1  twentieth  of  60  ?  14  twentieths  ? 

13.  How  many  times  1  in  19  eighths  ?  in  40  ninths  ? 
in  Q5  twelfths  ? 

14.  How  many  times  1  in  25  sevenths  ?  in  56 
tenths  ?  in  52  elevenths  ? 

15.  In  3  and  5  sevenths  how  many  sevenths  ? 

16.  In  6  and  3  eighths  how  many  eighths  ? 

17.  In  8  and  7  ninths  how  many  ninths  ? 

18.  In  9  and  3  twelfths  how  many  twelfths  ? 

19.  In  7  and  9  tenths  how  many  tenths  ? 

20.  If  10  pounds  of  sugar  cost  80  cents,  what  part 
of  80  cents  will  3  pounds  cost  ?  5  pounds  ? 

21.  If  a  man  earn  72  dollars  in  1  month,  how 
much  will  he  earn  in  1  fourth  of  a  month  ?  5  sixths  ? 

4  ninths  ?  7  eighths  ?  5  twelfths  ? 

22.  What  is  the  difference  between  7  eighths  of 
64  aiid  5  ninths  of  81  ? 


62  INTELLECTUAL   ARITHMETIC.  [39, 

23.  What  will  5  eiglitlis  of  a  bushel  of  chestnuts 
cost  at  10  cents  a  quart  ? 

24.  What  will  be  the  cost  of  4  sevenths  of  14 
dozen  of  eggs  at  11  cents  a  dozen  ? 

25.  If  James  has  108  cents,  and  Henry  has  7 
twelfths  as  many  and  20  cents  more,  how  many 
cents  has  Henry  ? 

26.  What  will  be  the  cost  of  1  ninth  of  a  hogs- 
head of  molasses  at  12  cents  a  quart  ? 

27.  Menzo,  having  48  dollars,  gave  1  sixteenth  of 
his  money  for  a  hat,  3  eighths  for  a  coat,  and  3 
twelfths  for  some  books  and  a  quarter's  tuition ;  how 
many  dollars  had  he  left  ? 

28.  A  man  bought  a  liorse  for  120  dollars  ;  he 
gave  7  tenths  as  much  for  a  carriage  as  he  paid  for 
the  horse,  and  3  sevenths  as  much  for  a  harness  as 
he  paid  for  the  carriage ;  how  much  did  the  whole 
cost  him  ? 

29.  If  a  man  put  200  dollars  at  interest,  and 
receive  3  twentieths  of  it  annually  for  its  use,  how 
many  dollars  does  he  receive  ? 

30.  If  a  vessel  sail  12  miles  an  hour,  how  many 
times  9  miles  will  she  sail  in  3  eighths  of  a  day  ? 

31.  Abel  has  49  marbles,  and  Alonzo  has  6  sevenths 
as  many  wanting  10  ;  how  many  has  Alonzo  ? 

32.  A  man,  having  300  cedar  posts,  sold  2  fifths 
of  them  to  A,  1  sixth  to  B,  3  tenths  to  C,  and  40 
posts  to  D  ;  hoAV  many  had  he  left  ? 

33.  What  will  be  the  cost  of  a  gold  watch  weigh- 
ing 1  third  of  a  pound  at  1  dollar  a  pennyweiglit  ? 

34.  What  will  be  the  cost  of  3  eighths  of  2  gallons 
of  wine  at  40  cents  a  pint  ? 

35.  A  grocer  bought  27  dozen  of  eggs  for  240 
cents,  and  sold  5  ninths  of  them  for  12  cents  a 
dozen,  and  the  remainder  for  1.0  cents  a  dozen  ;  how 
much  did  he  gain  by  the  operation  ? 


40.]  INTELLECTUAL   ARITHMETIC.  63 

40.     1.    9  is  1  fourth  of  what  number  ? 

Analysis.     9  is  1  fourth  of  4  titnes  9 ;  4  times  9  is 
S6.     Therefore  9  is  \  fourth  ofSQ, 

2.      7  is  1  fifth  of  what  number  ? 

8.  10  is  1  eiffhth  of  what  number  ? 

4.  12  is  1  tenth  of  what  number  I 

6.  20  is  1  half  of  what  number  ? 

6.  15  is  1  fourth  of  what  number  ? 

7.  30  is  1  sixth  of  what  number  ? 

8.  9  is  1  twelfth  of  what  number  ? 

9.  5  is  1  twentieth  of  what  number  ? 

10.  11  is  1  seventh  of  what  number  ? 

11.  9  times  4, and  3  fourths  of  4  are  how  many  ? 

12.  6  times  9,  and  7  ninths  of  9  are  how  many  ? 

13.  10  times  12,and  5  twelfths  of  12  are  how  mariy  ? 

14.  14  times  2, and  1  half  of  2  are  how  many  ? 

15.  8  times  ll,and  7  elevenths  of  11  are  how  many  ? 

16.  5  times  20,  and  13  twentieths  of  20  arc  how 
many  ? 

17.  64  are  how  many  times  8  ?  5  ?  12  ? 

18.  47  are  how  many  times  9?  10?  8?  6? 

19.  81  are  how  many  times  8  ?  9  ?  11  ?  12  ? 

20.  35  are  how  many  times  7?  6?  8?  9? 

21.  75  are  how  many  times  5?  6?  7?  9?  25? 

22.  3  fourths  of  16  are  how  many  times  6  ? 

Analysis.  3  fourths  oflQ  are  as  rtiany  times  6  as  6 
is  contained  tbnes  in  3  times  \  of  \Q  ;  1  fourth  of  16 
is  4,  and  3  times  4  is  12  ;  G  is  contained  in  12,  2  times, 
Tlierefore  o  fourths  oflQ  are  2  times  C. 

23.  6  tenths  of  100  arc  how  many  times  5  ? 

24.  5  twelfths  of  72  are  how  many  times  3  ?  4  ? 
G?  8? 

25.  7  ninths  of  03  —  3  eighths  cf  24  are  liow 
many  times  4  ?  5  ?  6  ?  7  ?  8  ? 

26.  11  twentieths  of  80  +  7  fifteenths  of  45  arc 
how  many  times  6  ?  7  ?  9  ?  12  ?  13  ? 


64  INTELLECTUAL   ARITHMETIC.  [41. 

4S.  1.  If  1  fourth  of  a  yard  of  cloth  cost  12 
cents,  what  will  1  yard  cost  ? 

Analysis.  Tf  I  fourth  of  a  yard  cost  12  cents,  4 
fourths,  or  1  yard,  to  ill  cost  4  tirnes  12  cents  ;  4  times 
12  cents  are  48  cents.  Therefore,  if  1  fourth  of  a  yard 
cost  12  cents,  1  yard  icill  cost  48  cer^^Js. 

2.  If  1  fifth  of  a  pound  of  tea  cost  10  cents,  what 
will  1  pound  cost  ? 

3.  If  1  third  of  a  gallon  of  molasses  cost  20  cents, 
what  will  1  gallon  cost  ? 

4.  20  is  1  third  of  what  number  ? 

5.  10  is  1  fifth  of  what  number  ? 

G.  If  1  lialf  of  a  cord  of  wood  cost  2  dollars,  what 
will  1  cord  cost  ?  what  will  2  cords  cost  ? 

7.  A  man  gave  2  shillings  for  his  dinner,  which 
was  1  twelfth  of  all  the  money  he  had ;  how  much 
money  had  he  ? 

8.  A  drover  rold  some  sheep,  and  gained  by  the 
sale  15  dollars,  which  was  1  fourth  of  what  the  sheep 
cost  him  ;  what  was  the  cost  of  the  sheep  ? 

9.  If  1  sixth  of  a  ton  of  hay  cost  3  dollars,  what 
will  3  sixths  cost  ?  5  sixths  ?  1  ton  ? 

10.  If  a  man  can  walk  6  miles  in  1  eighth  of  a 
day,  how  far  can  he  walk  in  1  day  ?  in  2  days  ?  in  3 
days  ? 

11.  James  had  40  plums,  and  divided  1  fourth  of 
them  equally  among  5  of  his  companions  ;  how  many 
did  he  give  to  each  ? 

12.  G  is  1  eighth  of  what  number  ? 

13.  15  is  1  fifth  of  what  number  ? 

14.  40  is  1  third  of  what  number  ? 

15.  1  fourth  of  40  is  how  many  times  5  ?  7  ? 

16.  1  sixth  of  00  is  how  many  times  4  ?  5  ?  6  ? 

17.  I  liave  16  dollars,  wliich  is  1  tliird  of  what  I 
paid  for  12  sheep ;  how  much  did  I  pay  a  head  ? 


4S.J  INTELLECTUAL   ARITHMETIC.  65 

18.  A  man  plowed  36  acres  of  his  farm ;  3 
fourths  of  this  was  just  equal  to  1  third  of  the  whole 
number  of  acres  in  his  farm ;  how  many  acres  in  his 
farm  ? 

19.  A  pole  stands  12  feet  in  the  water,  which  is  1 
fifth  of  the  length  of  the  pole  ;  how  long  is  the  pole  'i 

20.  Bouo-ht  a  watch  and  chain ;  for  the  chain  I 
gave  15  dollars,  which  was  1  fourth  of  what  I  paid 
for  the  watch  ;  what  did  they  both  cost  me  ? 

21.  If  1  twelfth  of  an  acre  of  land  cost  5  dollars, 
what  will  2  acres  cost  ? 


42,  1.  If  3  fourths  of  a  barrel  of  flour  cost  6 
dollars,  what  will  one  barrel  cost  ? 

Analysts.  If  3  fourths  of  a  barrel  of  four  cost  6 
(JoHars^  1  barrel  tcill  cost  4  times  1  third  of  6  dollars  / 
1  third  of  6  dollars  are  2  dollars,  and  4  times  2  dollars 
are  8  dollars.     Therefore,  (tc, 

2.  If  4  fifths  of  a  barrel  of  ale  cost  8  dollars, 
what  will  1  barrel  cost  ? 

3.  If  5  ninths  of  a  month's  wages  amount  tc  25 
dollars,  what  will  a  month's  wages  amount  to  ?  2 
months'  ? 

4.  What  will  1  barrel  of  flour  cost,  if  5  sevenths 
of  a  barrel  cost  10  dollars  ? 

5.  Sold  a  cow  for  25  dollars,  which  was  5  fourths 
of  what  she  cost  me ;  what  did  she  cost  me  ? 

6.  Bought  4  barrels  of  vinegar  at  6  dollars  a 
barrel,  which  was  but  8  ninths  of  its  real  value  ;  what 
was  its  real  value  per  barrel  ? 

7.  A  speculator  bought  some  pork  for  90  dollars, 
which  was  9  elevenths  of  what  he  sold  it  for ;  how 
much  did  he  gain  ? 

b 


66  INTELLECTUAL  ARITHMETIC.  [4S. 

8.  A  tailor  bought  two  pieces  of  cloth,  the  shorter 
piece  containing  24  yards  ;  5  eighths  the  number  of 
yards  in  the  shorter  piece  is  'ZO  yards  less  than  the 
number  of  yards  in  the  longer  piece ;  how  many 
yards  in  both  pieces  ? 

9.  If  7  tenths  of  an  acre  of  land  yield  28  bush- 
els of  wheat,  what  will  1  acre  yield  ?  what  will  3 
acres  yield  ? 

10.  16  is  4  fifths  of  what  number  ? 

AiSTALTsis.  16  is  4  fifths  of  5  times  1  fourth  o/  16  ; 
1  fourth  of  16  is  4,  and  5  times  4  is  20.  Therefore^  16 
is  4  fifths  of  20. 

11.  25  is  5  eighths  of  what  number  ? 

12.  14  is  7  twelfths  of  what  number  ? 

13.  9  is  3  tenths  of  what  number  ? 

14.  12  is  4  fifteenths  of  what  number  ? 

15.  20  is  2  sevenths  of  what  number  ? 

16.  18  is  6  elevenths  of  what  number  ? 

17.  21  is  3  halves  of  what  number  ? 

18.  72  is  9  eighths  of  what  number  ? 

19.  40  is  10  elevenths  of  what  number  ? 

20.  36  is  12  twentieths  of  what  number  ? 

21.  42  is  7  fifths  of  what  number  ? 

22.  5  sixths  of  24  is  2  thirds  of  what  number  ? 

Analysis.  5  sixths  of  24  is  2  thirds  of  3  times  1 
half  of  5  times  1  sixth  o/*  24 ;  1  sixth  of  24  is  4,  and 
5  times  4  is  20;  1  half  of  20  is  10,  and  3  ?/??ies  10  is 
80.     Therefore,  C  sixths  of  24  ?s  2  thirds  of  30. 

23.  3  fourths  of  16  is  6  sevenths  of  what  number  ? 

24.  4  fifths  of  30  is  8  elevenths  of  what  number  ? 

25.  6  fourths  of  28  is  7  ninths  of  what  number  ? 

26.  9  twelfths  of  60  is  5  thirds  of  what  number  ? 

27.  8  ninths  of  18  is  1  fourth  of  what  number  ? 

28.  11  fifteenths  of  45  is  3  halves  of  what  num- 
ber ? 


43.]  INTELLECTUAL   AEITHMETIC.  67 

29.  6  tenths  of  100  is  5  twelfths  of  what  number  ? 

30.  3  twentieths  of  80  is  2  sixteenths  of  wliat 
number  ? 

31.  9  eighths  of  64  is  8  fifths  of  what  number  ? 

32.  Of  a  certain  farm,  36  acres  are  woodland,  and 
5  sixths  of  the  woodland  is  3  fifths  of  the  number  of 
acres  of  cleared  land  ;  how  many  acres  of  cleared 
land,  and  how  many  acres  does  the  farm  contain  ? 

33.  Mr.  Smith  gave  5  sevenths  of  all  the  money 
he  had  for  a  horse  ;  he  then  paid  12  dollars  for  a 
saddle  and  bridle,  which  was  3  fourths  of  all  the 
money  he  had  left ;  how  much  money  had  he  at  first  ? 

34.  A  person,  being  asked  his  age,  answered  that 
if  he  were  twice  as  old,  1  third  of  his  age  would  be 
20  years  ;  how  old  was  he  ? 


43.  A  FRACTION  is  one  or  more  of  the  equal  parts  of 
a  unit.  Fractions  are  expressed  by  figures  in  the  following 
manner,  viz. :  — 

-J,  one  half.  f ,  two  thirds, 

i,  one  third.  f ,  three  fourths, 

i,  one  fourth.  -J,  seven  eighths. 

^,  one  fifth.  y^Q-,  nine  tenths. 

^,  one  sixth.  l-|-,  eleven  twelfths. 

-1-,  one  seventh.  ^-J,  thirteen  twentieths. 

1,  one  eighth.  4|,  four  and  1  seventh. 

-Jq-,  one  tenth.  9f ,  nine  and  5  eighths,  &c. 

1.  The  number  below  the  short  horizontal  line  is 
called  the  denominator. 

2.  The  number  above  the  line  is  called  the  numer- 
ator. 

3.  The  denominator  shows  into  how  many  parts 
the  whole  thing  is  di\dded. 


68  INTELLECTUAL   ARITHMETIC.  [43. 

4.  The  numerator  shows  how  many  of  these  parts 
are  taken  or  used. 

5.  A  proper  fraction  is  one  whose  numerator  is 
less  than  the  denominator ;  its  value  is  less  than  a 
unit. 

G.  An  improper  fraction  is  one  whose  numerator 
is  equal  to,  or  greater,  than  the  denominator ;  its 
value  is  equal  to,  or  g-r eater,  than  a  unit. 

7.  A  7)iixed  number  is  a  whole  number  joined  with 
a  fraction. 

8.  What  kind  of  a  fraction  is  |  ?  What  is  the  4 
called  ?     What  does  it  show  ? 

9.  In  the  fraction  |,  what  is  the  3  called  ?  W^hat 
does  it  show  ? 

10.  Into  how  many  equal  parts  must  a  thing  be 
divided  to  produce  the  fraction  |  ?  how  many  of 
these  parts  must  be  taken  ? 

11.  What  kind  of  a  fraction  is  ^  ?     Why  ? 

12.  What  kind  of  a  number  is  6|  ?     Why  ? 

13.  How  would  you  obtain  |-  of  any  thing  ? 

14.  Plow  would  you  obtain  |  of  any  thing  ? 

15.  How  many  times  ^  in  6  ? 

Analysis.  Since  in  1  there  are  4  times  ^,  or  |-,  in  6 
there  are  6  times  f ,  or  ^^-.  Therefore  there  are  24  times  ^ 
in  6. 

16.  How  many  times  ^  in  4  ?  in  8  ?  in  9  ?  in  12  ? 

17.  How  many  times  ^  in  3  ?  in  5  ?  in  7  ?  in  8  ? 

18.  How  many  times  l  in  2  ?  in  4  ?  in  5  ?  in  7  ? 

19.  How  many  times  ^V  in  5  ?  in  6  ?  in  7  ?  in  9  ? 

20.  How  many  times  ^V  in  3  ?  in  4  ?  in  6  ?  in  7  ? 

21.  How  many  times  |  in  3|  ?  in  4|  ?  in  7^  ? 

22.  How  many  times  |  in  2^  ?  in  5|  ?  in  6^  ? 

23.  How  many  times  -^^  in  Br^^  ?  in  7^^q^  ?  in  8f^  ? 


44.]  INTELLECTUAL   ARITHMETIC.  69 

24.  In  121   how  many  thirds  ? 

25.  In  7 1  how  many  fifths  ? 

26.  In  10 1  how  many  eighths  ? 

27.  In  9-^  how  many  twelfths  ? 

28.  In  15|-  how  many  fourths  ? 

29.  Reduce  20 1  to  an  improper  fraction. 
80.  Reduce  8|^  to  an  improper  fraction. 

31.  Reduce  7}|-  to  an  improper  fraction. 

32.  Reduce  8-^  to  an  improper  fraction. 

33.  Reduce  25-|  to  an  improper  fraction. 

34.  How   do   you   reduce  a   whole  number  to  a 
fraction  having  a  required  denominator  ? 

35.  How  do  you  change  a  mixed  number  to  an 
improper  fraction  ? 


44.     1.    In  \^  how  many  times  1  ? 

Analysis.  Since  ^  equal  1,  \^--  are  as  mam/  times  1 
as  I  are  contained  times  in  -y-;  |  are  contained  in  J/-,  4 
times.     Therefore  Y  <^^^'6  4  times  1,  cr  4. 

2.  In  -2^^-  how  many  times  1  ? 

3.  In  ^^-  how  many  times  1  ? 

4.  In  ^-  how  many  times  1  ? 

5.  In  ^^  how  many  times  1  ? 

6.  In  If  how  many  tim.es  1  ? 

7.  In  J-P"  how  many  times  1  ? 

8.  How  many  times  1  in  \^  ?  in  |-§-  ?  in  -|-J  ? 

9.  How  many  times  1  in  ^-  ?  in  ^y^-  ?  in  -^  ? 

10.  How  many  times  1  in  -^  ?  in  ^^1  in  \\  ? 

11.  How  many  times  1  in  ^-§-  ?  in  J^  ?  in  -LiA  ? 

12.  How  many  times  1  in  11^  ?  in  %"  •  "^  ^P-? 

13.  How  many  times  1  in  -9/  ?  in  -^^a  ?  in  4f '? 

14.  How  many  times  1  in  ff  ?  in  -^2^  ?  in  %-  ? 


TO  INTELLECTUAL   ARITHMETIC.  [45, 

15.  How  many  times  1  in  |-|  ?  in  |-|  ?  in  ^'^-^-  ? 

16.  How  do  you  reduce  an  improper  fraction  to  a 
whole  or  mixed  number  ? 

17.  Reduce  |^|  to  an  equivalent  whole  number. 

18.  Reduce  J^V"  ^^  ^^^  equivalent  mixed  number. 

19.  Reduce  -^^^  to  an  equivalent  mixed  number. 

20.  Reduce  ^gO-  to  an  equivalent  mixed  number. 

21.  Express  the  value  of  ^^-^  in  a  whole  number. 

22.  Express  the  value  of  ^^^  in  a  mixed  number. 

23.  Express  the  value  of  ^-  in  a  mixed  number. 


4«5. 


1.    In  I  of  Ij  how  many  sixths  ? 


Analysis.  Smce  in  1  there  are  |,  in  |  of  ly  there 
are  2  times  i  o/  | ;  |  o/  §  ^s  |,  wid  2  ifmes  |  are  ^. 
There/ore,  dbc. 

2.  In  I  of  1   how  many  tenths  ? 

8.  In  I  of  1   how  many  twentieths  ? 

4.  In  1^  of  1  how  many  fortieths  ? 

5.  In  I  of  1   how  many  tenths  ? 

6.  In  -|  of  1   how  many  sixteenths  ? 

7.  In  I  of  1   how  many  twenty-firsts  ? 

8.  In  ^  of  1   how  many  thirty-sixths  ? 

9.  In  I  of  1   how  many  twelfths  ? 

10.  In  I  of  1   how  many  twenty-fifths  ? 

11.  In  -^.j  of  1   how  many  sixtieths  ? 

12.  In  4-  of  1  hov/  many  eighteenths  ? 

13.  In  -^Q  of  1   how  many  fortieths  ? 

14.  In  0%  of  1   how  many  eightieths  ? 

15.  In  i|  of  1   how  many  thirtieths  ? 

16.  In  f  of  1   how  many  eighths  ? 

17.  In  I  of  1  how  many  fourteenths  ? 


45.]  INTELLECTUAL   ARITHMETIC.  71 

18.  In  f  of  1  how  many  twenty-sevenths  ? 

19.  In  I  of  1   how  many  fifty-sixths  ? 

20.  In  -^j  of  1  how  many  forty-fourths  ? 

21.  In  IJ-  of  1   how  many  thirty-seconds  ? 

22.  In  ^-^  of  1  how  many  eightieths  ? 

23.  In  If  of  1  how  many  ninetieths  ? 

24.  In  II  of  1  how  many  one  hundred  twentieths  ? 

25.  How  many  sixths  in  |-|  ? 

Analysis.     Since  in  1  there  are  ^^f,  in  ^  of  \  are  ^  of 
tI'  ^^  t\  5  ^^^^  A  ***  contained  in  \^,  5  <me«.     Therefore 


in  ^1  «re  5  sixths. 
26. 

27. 


How  many  eighths  in  ^^  ?  in  ^|  ? 

^ t .  How  many  fourths  in  ||  ?  in  y^2  • 

28.  How  many  thirds  in  ^  ?  in  H  ? 

29.  How  many  sevenths  in  -|~|  ?  in  ^\  ? 

30.  How  many  twelfths  in  ||  ?  in  ^|-  ? 

31.  How  many  ninths  in  |J  ?  in  ||  ? 

32.  How  many  sixths  in  ^|-  ?  in  ^|  ? 

33.  How  many  eighths  in  |J  ?  in  |J  ? 

34.  How  many  fourteenths  in  ^|  ?  in  |-^  ? 

35.  How  many  fifths  in  |f  ?  in  |^  ? 

36.  How  many  sevenths  in  ||-  ?  in  ||  ? 

37.  How  many  fourths  in  ||  ?  in  l|  ? 

38.  How  many  sixths  in  |§  ?  in  f|  ? 

39.  How  many  halves  in  ||  ?  in  |f  ? 

40.  How  many  tenths  in  |4  ?  in  ||  ? 

41.  How  many  fifteenths  in  |i  ?  in  f  f  ? 

42.  How  many  elevenths  in  ||  ?  in  ^  ? 

43.  How  many  sixteenths  in  |f  ?  in  |f  ? 

44.  How  many  twentieths  in  -^^-^  ?  in  ^^  ? 

45.  How  many  twenty-fourths  in  ||  ?  in  -^^^  ? 


72  INTELLECTUAL   ARITHMETIC.                    [46. 

46.     1.   Eeduce  -f^  to  its  lowest  terms. 

NoTB.  A  fraction  is  said  to  be  in  its  lowest  terms  when  no  number 
greater  than  1  will  exactly  divide  both  numerator  and  denominator. 

2.  Reduce  -^^  to  its  lowest  terms. 

3.  Reduce  ^-|  to  its  lowest  terms. 

4.  Reduce   |^  to  its  lowest  terms. 
6.  Reduce  ^-^-  to  its  lowest  terms. 

6.  Reduce  ||  to  its  lowest  terms. 

7.  Reduce  ||  to  its  lowest  terms. 

8.  Reduce  ^-^  to  its  lowest  terms. 

9.  Reduce  ||   to  its  lowest  terms. 

10.  Reduce  H  to  its  lowest  terms. 

11.  Reduce  |^^  to  its  lowest  terms. 

12.  Reduce  -f^Q  to  its  lowest  terms. 
18.  Reduce  -|^  to  its  lowest  terms. 

14.  Reduce  -|f  to  its  lowest  terms. 

15.  Reduce  M-  to  its  lowest  terms. 

16.  Reduce  -f-^^  to  its  lowest  terms. 

17.  Reduce  J-|^  to  its  lowest  terms. 

18.  Reduce  -f^-^  to  its  lowest  terms. 

19.  Reduce   ||  to  its  lowest  terms, 

20.  Reduce   |J-  to  its  lowest  terms. 

21.  Reduce  -^^^  to  its  lowest  terms. 

22.  Reduce  ^^  to  its  lowest  terms. 

23.  How  do  you  reduce  a  fraction  to  its  lowest 
terms  ? 


Remarks.  1.  If  the  numerator  be  multiplied  by  any  number,  the 
value  of  the  fraction  will  be  multiplied  as  many  times  as  there  are  units 
in  the  multiplier, 

2.  If  the  numerator  be  divided  by  any  number,  the  value  of  the  fraction 
will    be  divided  as    many  times  as  there  are  units  in  the  divisor. 

3.  If  the  denominator  be  multiplied  by  any  number,  the  value  of  the 
fract;io)[i  wU\  be  divided  as  many  times  as  there  are  wnits  in  the  multi- 
pliof. 


47.]  INTELLECTUAL    ARITHMETIC.  T3 

4:7,  Fractions  are  said  to  have  a  common  denominator 
when  their  denominators  are  alike.  Any  number  that  can 
be  divided  by  each  of  the  denominators  of  the  given  frac- 
tions may  be  taken  for  the  common  denominator. 

1.  Reduce  \  and  |  to  fractions  having  a  common 
denominator. 

Analysis.  12  is  exactly  divisible  by  4  and  3,  and  may 
therefore  be  taJcen  for  a  common  denominator.  Since  in  1 
there  are  ^f,  in  ^  of  \  there  must  be  ^  of  ^f ,  or  -^^^  and  in 
%  of  1  there  must  be  |  of  -if,  or  -f^.  Therefore  ^  and  f 
are  equal  to  -^^  and  -^^. 

2.  Reduce  J  and  |  to  fractions  having  a  common 
denominator. 

3.  Reduce  -I  and  -l  to  a  common  denominator. 

4.  Reduce  ^-  and  |  to  a  common  denominator. 

5.  Reduce  |  and  |-  to  a  common  denominator. 

6.  Reduce  f  and  J  to  a  common  denominator. 

7.  Reduce  |-  and  |  to  a  common  denominator. 

8.  Reduce  |,  -|,  and  ^  to  a  common  denominator. 

9.  Reduce  | ,  ^,  and  -^^  to  a  common  denominator. 

10.  Reduce  -j\,  -^^  and  |^  to  a  common  denomi- 
nator. 

11.  Reduce  -|-,  -f^  and  |  to  a  common  denominator. 

12.  Reduce  f ,  |,  f  and  |  to  a  common  denomi- 
nator. 

13.  Reduce  -^-^,  -^  and  -g\  to  a  common  denomi- 
nator. 

14.  Reduce  1|-,  2^  and  f  to  a  common  denomi- 
nator. 

4.  If  the  denominator  be  divided  by  any  number,  the  value  of  the  frac- 
tion will  be  multiplied  as  many  times  as  there  are  units  in  the  divisor. 

5.  If  both  numerator  and   denominator   be   multiplied  by  the  same 
number,  the  value  of  the  fraction  will  not  be  changed. 

6.  If  both  numerator  and  denominator  be  divided  by  the  same  number, 
the  value  of  the  fraction  will  net  be  changed. 


74  INTELLECTUAL   ARITHMETIC.  [48. 

48 •  1.  James  has  f  of  a  dollar,  John  -|  of  a 
dollar,  and  George  |  of  a  dollar ;  how  many  fifths 
of  a  dollar  have  they  all  ?   how  many  dollars  ? 

Analysis.  They  all  have  the  sum  o/  f  +  f  -f-  f?  equal 
to  JgO-  dollars,  equal  to  2  dollars.      Therefore,  ^c, 

2.  Jane  had  |  of  a  dollar  and  her  father  gave 
her  I  of  a  dollar  more  ;  how  mnch  had  she  then  ? 

3.  Austin  buys  a  pair  of  skates  for  |^  of  a  dollar, 
a  pair  of  mittens  for  |  of  a  dollar,  and  a  slate  for  |- 
of  a  dollar  ;  what  is  the  cost  of  all  ? 

4.  A  grocer  sold  ^  dozen  eggs  to  one  man,  |^  of  a 
dozen  to  another,  and  |  of  a  dozen  to  another ;  how 
many  dozen  did  he  sell  to  all  ? 

Note.     Fractions  having  different  denominators  must  be  reduced  to  a 
common  denominator  before  adding  or  subtracting. 

5.  Mary  paid  |  of  a  dollar  for  some  ribbon,  |  of 
a  dollar  for  a  pair  of  gloves  and  l  of  a  dollar  for  a 
pair  of  hose  ;  what  was  the  cost  of  the  whole  ? 

6.  Sold  |-  of  an  acre  of  land  to  one  man,  -|  to 
another  and  -^^  to  another ;  how  much  was  sold 
to  all? 

7.  A  laborer  dug  |-  a  rod  of  ditch  the  first  hour, 
I  of  a  rod  the  second,  |  the  third  and  -^^  the  fourth  ; 
how  many  rods  did  he  dig  in  4  hours  ? 

8.  A  farmer  sold  ^  of  his  grain  to  one  man,  |  to 
another,  and  -J  to  another  ;  what  part  of  his  grain 
did  he  sell  ? 

9.  Henry  paid  |  of  a  dollar  for  a  sled,  i  a  dollar 
for  a  kite  and  J  of  a  dollar  for  a  string ;  what  was 
the  cost  of  the  whole  ? 

10.  Emma  paid  2^  dollars  for  a  dress,  1|  dollars 
for  a  pair  of  shoes  and  -J  of  a  dolkir  for  some  ribbon  ; 
what  was  the  cost  of  the  whole  ? 

Note.     Add  the  whole  numbers  and  the  fractions  separately,  and  then 
unite  their  sums. 


48.]  INTELLECTUAL   ARITHMETIC.  75 

11.  Milton  saved  f  of  a  dollar  one  week,  |  of  a 
dollar  the  next,  1|  the  next  and  2J  the  next ;  how 
much  did  he  save  in  4  weeks  ? 

12.  Albert  picked  2^  bushels  of  apples  from  one 
tree,  3|  from  another  and  3|-  from  another  ;  how 
many  bushels  did  he  pick  from  the  3  trees  ? 

13.  If  it  take  4  J  yards  of  cloth  for  a  coat,  2 J  yards 
for  a  pair  of  pantaloons,  and  ^  of  a  yard  for  a  vest, 
how  many  yards  of  cloth  will  it  take  for  the  whole  ? 

14.  If  a  man  walk  12f  miles  in  the  forenoon  and 
101-  miles  in  the  afternoon,  how  many  miles  does  he 
walk  during  the  day  ? 

15.  Harvey  bought  a  sled  for  62|-  cents  and  sold 
it  for  12^  cents  more  than  he  gave  for  it ;  how  much 
did  he  receive  for  it  ? 

16.  Three  men  bought  a  horse.  A  paid  25^^ 
dollars,  B  paid  30|  dollars  and  C  paid  35|  dollars ; 
what  was  the  cost  of  the  horse  ? 

17.  If  coal  is  worth  5y^g  dollars  a  ton,  and  wood 
is  worth  3yV  dollars  a  cord,  what  will  be  the  cost  of 
one  ton  of  coal  and  two  cords  of  wood  ? 

18.  Find  the  sum  of  -^^  and  ■^. 

19.  Find  the  sum  of  f ,  -|   and  1. 

20.  Find  the  sum  of  -|,  f  and  -f^. 

21.  Find  the  sum  of  -^^^  tV  ^^^^  f  • 

22.  Find  the  sum  of  -J,  ^  and  \. 

23.  Add  together  f ,  ^  and  -f-^. 

24.  Add  together  ■^,  -^-^   and  -|. 

25.  Add  together  y^g-,  -|,  -f^  and  -J. 

26.  Add  together  y\,  f  and  |. 

27.  Add  together  |,  l,  -f^  and  1. 

28.  Add  together  |-,  J,  ^,  ^  and  i. 

29.  What  is  the  sum  of  2^  and  31  ? 

30.  What  is  the  sum  of  81  and  121  ? 


76  INTELLECTUAL   ARITHMETIC.  [49, 

31.  What  is  the  sum  of  14i,  lOf ,  and  5-J-  ? 

82.  What  is  the  sum  of  7^^^^  +  15|  -\-  iOJ  ? 

33.  What  is  the  sum  of  25-|-  +  13|  +  5^^  ? 

34.  What  is  the  sum  of  6|  +  7-f  +  4|  ? 

35.  What  is  the  sum  of  ^a^.  -|-  li_i  _|.  141  _|.  iqi  ? 
86.  What  is  the  sum  of  S~^  _f-  5 1  -f  |  _|_  iQi  ? 

37.  AVhat  is  the  sum  of  6  +  14^^  +  H^  +  i\  ? 

38.  What  is  the  sum  of  20  +  7 ^^  +  l-|-i  ? 


40.  1.  Amos  having  |  of  a  dollar,  gave  |  of  a 
dollar  to  a  beggar ;  how  much  had  he  left  ? 

Analysis.  He  had  left  the  difference  hetivecn  -|  and  f 
of  a  dollar  ;  f  —  -|  =  f  o/*  a  dollar.     Therefore,  8^c. 

2.  Norman  had  -J  of  a  bushel  of  peaches  ;  he  sold 
■|  of  a  bushel ;  what  part  of  a  bushel  had  he  left  ? 

3.  Nancy  paid  |  of  a  dollar  for  a  geography  and 
■|  of  a  dollar  for  a  philosophy  ;  for  which  did  she  pay 
the  more,  and  how  much  ? 

4.  Two  men  own  a  piece  of  property  together ; 
one  owns  |-  of  it ;  how  much  does  the  other  own  ? 

5.  When  rye  is  worth  J  of  a  dollar  per  bushel 
and  corn  is  worth  |-  of  a  dollar,  what  is  the  differ- 
ence in  the  price  ? 

6.  A  grocer  sells  1  of  a  box  of  tea  from  a  box  f 
full ;  what  part  of  the  whole  box  is  left  ? 

7.  Henry  can  run  |-  of  a  mile  in  the  same  time 
that  John  can  run  ^ ;  which  runs  the  farther,  and 
how  much  ? 

8.  Parley  gave  |-  of  a  dollar  for  a  vest  and  |  of  a 
dollar  for  a  pair  of  shoes ;  what  was  the  difference 
in  the  cost  ? 

9.  A  gentleman,  owning  a  boat,  sold  -^  of  it; 
how  much  of  it  did  he  still  own  ? 


49.]  INTELLECTUAL   AKITHMETIC.  77 

10.  If  Robert  earn  7-|  dollars  a  week  and  Her- 
man earn  6  J-  dollars  a  week,  how  much  more  than 
Herman  does  Robert  earn  ? 

11.  Arthur  gathered  10 J  quarts  of  chestnuts  and 
sold  Y|-  quarts ;  how  many  quarts  had  he  left  ? 

12.  From  a  piece  of  cloth  containing  12^  yards, 
5|-  yards  were  cut ;  how  many  yards  remained  ? 

13.  If  I  put  15|  dollars  in  the  bank  at  one  time, 
how  much  must  I  afterwards  put  in  to  make  the  sum 
20  dollars  ? 

14.  From  a  hogshead  of  molasses,  9  3-  gallons  were 
drawn  ;  how  many  gallons  remained  ? 

15.  Edgar  will  be  14  years  old  B^j  years  hence ; 
how  old  is  he  now  ? 

16.  From  a  jug  of  molasses  containing  1  gallon, 
■J  of  a  quart  was  used  ;  how  much  was  left  ? 

17.  If  I  buy  a  book  for  f  of  a  dollar,  how  much 
change  must  be  returned  to  me  for  a  3  dollar  bill  ? 

18.  A  lady,  liaving  18 1  dollars,  bought  a  bonnet 
for  5^  dollars  ;  how  much  money  had  she  left  ? 

19.  What  is  the  difference  between  |  and  |  ? 

20.  What  is  tlie  difference  between  ^  and  I  ? 

21.  What  is  the  difference  between  -f-^  and  |  ? 

22.  What  is  the  difference  between  1^  and  |  ? 

23.  What  is  the  difference  between  3|  and  11  ? 

24.  What  is  the  difference  between  16|  and  9^  ? 

25.  What  is  the  difference  between  20  and  12 J  ? 

26.  How  many  are  ^  —  |  ? 

27.  How  many  are  if  —  -J  ? 

28.  How  many  are  12  —  6^^  ? 

29.  How  many  are  36|-  —  24f  ? 

30.  How  many  are  25^  —  10  J  ? 

31.  How  many  are  16  —  9|  ? 

32.  How  many  are  28  —  17f  ? 


78  INTELLECTUAL   ARITHMETIC.  [50. 

50,  1.  Mr.  Smith  sold  ^  of  his  estate  to  A,  l  of 
it  to  B  and  ^  to  C  ;  what  part  remained  unsold  ? 

2.  A  gambler  lost  in  play  ^  and  ^-  of  his  money ; 
what  part  had  he  left  ? 

3.  A  lady  paid  J-  of  her  money  for  a  bonnet,  ^  for 
a  shawl  and  ^  for  a  pair  of  gaiters ;  what  part  had 
she  left  ? 

4.  A  laborer  worked  3  days  for  1^,  |*  and  1|  dol- 
lars ;  had  he  received  2  dollars  a  day,  how  much 
more  would  he  have  received  ? 

5.  From  a  piece  of  calico  containing  32|  yards, 
two  dress  patterns  were  cut,  one  containing  lOJ 
yards  and  the  other  12|  yards  ;  how  many  yards 
remained  in  the  piece  ? 

6.  I  deposited  in  the  bank  at  one  time  $20|^,  at 
another  ^15  J ;  how  much  more  must  I  deposit  to 
make  the  amount  $50  ? 

7.  Paid  $G|  for  a  barrel  of  flour,  $5|  for  a  ton  of 
coal,  and  gave  in  payment  a  10  dollar  bill  and  a  5 
dollar  bill ;  how  much  change  must  be  returned  to 
me  ? 

8.  A  merchant  bought  5  barrels  of  flour,  at  815  a 
barrel,  and  paid  $4:5-^-q  in  goods  and  the  remainder 
in  cash  ;  how  much  cash  did  he  pay  ? 

9.  If  you  divide  $80  among  three  men,  giving  the 
first  J  of  it,  and  the  second  |35|,what  will  the  third 
receive  ? 

10.  A  farmer,  having  120  bushels  of  oats  to  sell, 
sold  15 J  bushels  more  than  ^  of  them  at  one  time, 
and  20  bushels  less  than  |^  of  them  at  another  time ; 
how  many  bushels  had  he  left  ? 

11.  Asaph  gave  -|  of  his  money  for  a  sled,  |  for  a 
cap,  and  had  39  cents  left ;  how  much  had  he  at  first  ? 

12.  Morgan  is  lOf  years  old,  Myron  is  9-|  years 
old,  and  the  sum  of  their  ages  is  5J  years  more  than 
Martin's  age ;  how  old  is  Martin  ? 


550.]  INTELLECTUAL  ARITHMETIC.  V9 

13.  James  is  9 J  years  old,  and  Lewis  is  5^  years 
less  than  twice  as  old  as  James ;  what  is  the  differ- 
ence in  their  ages  ? 

14.  A  man,  having  ^64,  bought  3  cows  ;  for  the 
first  cow  he  gave  -^  of  it,  for  the  second  |  of  it,  and 
the  remainder  for  the  third ;  what  was  the  cost  of 
the  third  cow  ? 

15.  A  grocer  drew  from  a  hogshead  20|  gallons 
of  molasses  at  one  time,  and  25-J  gallons  at  another ; 
how  many  gallons  remained  ? 

16.  What  number  must  be  taken  from  36  that  the 
remainder  may  be  T|-  ? 

17.  From  what  number  must  9^  be  taken  to  leave 

193  ? 

18.  What  number  must  be  added  to  16^^q-  that 
the  sum  may  be  2of  ? 

19.  A  person  being  asked  his  age,  replied  that  if 
4|  years  were  added  to  12^  years,  the  sum  would  be 
^  his  age  ;  what  was  his  age  ? 

20.  A  person,  undertaking  a  journey  of  60  miles, 
traveled  ^  of  the  distance  the  first  day,  ^  of  the 
remainder  the  second  day,  and  |-  of  the  remainder 
the  third  day ;  how  far  from  his  place  of  destination 
was  he  at  the  close  of  the  third  clay  ? 

21.  What  is  the  difference  between  1T|  and  5^- 

22.  What  is  the  difference  between  25 1^  and  11 J 

+  7|? 

23.  What  is  the  difference  between  9  +  12|   and 

82  _|_  41 9 

24.  From  30^  take  201  _j_  SJL.. 

25.  From  40  —  lOf  take  71  +  51. 

26.  From  281  take  211  _  5|. 

27.  From  f  +  i  +  f  take  1  +  f  +  tV- 

28.  From  3  +  f  +  f  take  l^j. 


80  INTELLECTUAL   ARITHMETIC.  [51. 

51.  1.  What  will  5  pounds  of  tea  cost  at  |  of  a 
dollar  a  pound  ? 

Analysis.  Since  1  pound  cost  |-  of  a  dollar,  5  pounds, 
'which  are  5  times  1  pound,  ivill  cost  b  times  f ,  or  -L^,  of  a 
aollar,  equal  to  $3f .  Therefore  5  pounds  of  tea,  at  ^  of  a 
dollar  a  pound,  will  cost  $3|-. 

2.  What  cost  4  yards  of  linen  at  |  of  a  dollar  a 
yard  ? 

3.  When  sugar  is  }  of  a  dollar  a  pound,  what  will 
25  pounds  cost  ? 

4.  If  |-  of  a  pound  of  butter  last  a  family  1  day, 
how  many  pounds  will  last  them  one  week  ? 

5.  What  will  be  the  cost  of  10  peaches  at  |-  of  a 
cent  apiece  ? 

6.  If  a  man  earn  -^^  of  a  dollar  a  day,  how  much 
will  he  earn  in  12  days  ? 

7.  If  1  peck  of  pears  cost  J-  of  a  dollar,  what  will 
2  bushels  cost  ? 

8.  How  many  loaves  of  bread  must  you  give  to  8 
beggars,  if  you  give  them  |-  of  a  loaf  apiece  ? 

9.  At  I  of  a  dime  a  pound,  what  will  15  pounds 
of  nails  cost  ? 

10.  What  will  9  yards  of  silk  cost  at  ^J  of  a  dollar 
a  yard  ? 

11.  George  had  |^  of  a  dollar,  and  William  had  8 
times  as  much  ;  how  much  had  William  ? 

12.  If  1  horse  eat  |  of  a  ton  of  hay  in  a  month, 
how  much  will  10  horses  eat  ? 

13.  How  many  are  9  times  f  ?  12  times  |  ?  14 
times  ^^3  ?  20  times  -^  ? 

14.  if  1  man  can  reap  |  of  an  acre  of  rye  in  a 
day,  how  much  can  11  men  reap  ? 

15.  How  many  barrels  of  flour  will  be  given  to  9 
poor  families,  if  each  receive  -^  of  a  barrel  ? 

16.'  How  many  are  12  times  -^  ?  16  times  ^  ? 


5S.]  INTELLECTUAL   ARITHIylETIC.  81 

17.  Bought  6  bushels  of  corn  at  $|  a  bushel,  and 
had  84  left ;  how  mucli  money  had  1  at  first  ? 

18.  If  1  quart  of  molasses  cost  $^Qy  what  will  4 
gallons  cost  at  tlie  same  rate  ? 

ly.  If  a  boy  give  each  of  his  4  companions  |  of  a 
quart  of  chestnuts,  and  have  4-J-  quarts  left,  how 
many  quarts  had  he  at  first  ? 

20.  How  do  you  multiply  a  fraction  by  a  whole 
number  ? 


52,  1.  If  1  box  of  raisins  cost  82|,  what  will  5 
boxes  cost  ? 

Analysis.  7/"  1  box  of  raisuis  cost  $2f ,  5  boxes,  which 
are  5  times  1  box,  will  cost  5  tifnes  $2|^ ;  5  ti?7ies  |  are  \^, 
or  $3f;  5  times  m  are  $10;  %^  added  to  $10  are 
$lof.  Tlierefore,  if  1  box  of  raisins  cost  $2f,  5  boxes 
will  cost  $13|. 

2.  At  12|^  cents  a  pound,  what  will  9  pounds  of 
butter  cost  ? 

3.  At  86 J  a  barrel,  what  will  7  barrels  of  flour 
cost  ? 

4.  How  many  bushels  of  grain  will  15  bags  hold, 
if  they  hold  2i  bushels  apiece  ? 

5.  What  will  be  the  cost  of  12  pounds  of  rice,  at 
6|  cents  a  pound  ? 

6.  What  will  9  dozen  of  eggs  cost  at  11|-  cents  a 
dozen  ? 

7.  AVhat  will  7  yards  of  cloth  cost  at  ^^^q  a  yard  ? 

8.  If  1  barrel  of  fish  cost  814|,  what  will  6  barrels 
cost  ? 

9.  If  1  horse  eat  3  J  tons  of  hay  in  5  months,  how 
many  tons  will  20  horses  eat  in  the  same  time  ? 

10.  If  1  pint  of  wine  cost  81  J,  what  will  1  gallon 
cost  ? 


8a  INTELLECTUAL   ARITHMETIC.  [53. 

11.  If  5  men  can  do  a  piece  of  work  in  10 1  days, 
how  long  will  it  take  1  man  to  do  the  same  ? 

12.  If  a  grain  of  gold  is  worth  4^  cents,  what  is  1 
pennyweight  worth  ? 

13.  A  grocer  sold  9  pounds  of  coffee  at  121  cents 
a  pound,  and  7  pounds  of  sugar  at  8|  cents  a  pound ; 
how  much  did  he  receive  for  both  ? 

14.  If  it  take  3f  yards  of  cloth  for  a  coat,  and  2^ 
yards  for  a  pair  of  pantaloons,  how  many  yards  will 
be  required  to  make  3  of  each  ? 


53.  1.  If  1  pound  of  cheese  cost  10  cents,  what 
will  5|  pounds  cost  ? 

Analysis.  Since  1  pound  cost  10  cents,  5|  pounds, 
which  are  5|  times  1  pound,  ivill  cost  5|  tirnes  10  cents  ; 
5  times  10  cents  are  50  cents,  |  q/'  10  cents  are  3  times  ^  of 
10  cents  ;  ^  of  10  cents  is  If  cents,  and  |  of  10  cents  are  3 
times  \^  cents,  or  2)%  cents,  which  added  to  50  cents  make 
53|^  cents.     Therefore,  S^c. 

2.  If  a  horse  travel  6  miles  an  hour,  how  far  will 
he  travel  in  7|  hours  ? 

3.  If  a  person's  expenses  be  |12  a  week,  what 
will  they  be  for  9f  weeks  ? 

4.  What  will  4|  barrels  of  cider  cost  at  $3  a  barrel  ? 

5.  What  will  10|  pounds  of  honey  cost  at  12  cents 
a  pound  ? 

6.  What  will  15|  bushels  of  potatoes  cost  at  6 
shillings  a  bushel  ? 

7.  If  a  pint  of  wine  is  worth  40  cents,  what  are  3| 
pints  wortli  ? 

8.  If  a  man  can  build  4  rods  of  wall  in  a  day,  how 
many  rods  can  he  build  in  7|  days  ? 

9.  If  a  barrel  of  flour  last  a  family  6  weeks,  how 
long  will  4J  barrels  last  them  'i 


53.]  INTELLECTUAL   ARITHMETIC.  83 

10.  If  stage  fare  is  4  cents  a  mile,  what  will  it 
cost  to  ride  20 1  miles. 

11.  If  a  merchant  pay  12  shillings  for  3  caps,  and 
sell  them  for  6|  shillings  apiece,  what  is  his  gain  ? 

12.  Bought  9 1  yards  of  silk  at  12  shillings  a 
yard,  and  12|  pounds  of  tea  at  7  shillings  a  pound ; 
how  much  more  did  the  silk  cost  than  the  tea  ? 

13.  If  I  buy  8 1  tons  of  coal,  at  $5  a  ton,  how 
much  less  than  $50  will  it  cost  ? 

14.  A  woman  took  6|  dozen  eggs  to  market, 
which  she  sold  for  12  cents  a  dozen  ;  she  received  in 
payment  44  yards  of  calico  at  10  cents  a  yard,  3-J 
yards  of  ribbon  at  8  cents  a  yard ;  how  much  was 
still  her  due  ? 

15.  If  |-  of  a  barrel  of  flour  last  a  family  1  month, 
how  many  barrels  will  last  8  such  families  G-|  months  ? 

16.  What  is  the  product  of  4^-  times  9  multiplied 
by  3  ?  ^ 

17.  What  is  the  product  of  5  times  3|-  multi- 
plied by  2|-  ? 

18.  Multiply  U  times  10  by  |  of  15. 

19.  Multiply  3-J-  times  6  by  -}oi  24:. 

20.  Multiply  4|  by  |  of  16. 

21.  Multiply  2  times  9J  by  2J  times  4. 

22.  Multiply  5  times  SJ  by  |  of  15. 

23.  What  is  the  sum  of  8  times  l-f^  and  4| 
times  12  ? 

24.  What  is  the  sum  of  6|  times  11  and  12 
times  5|-  ? 

25.  What  is  the  difference  between  4|  times  10 
and  3  times  9|  ? 

26.  What  is  the  difference  between  7  times  8  J-  and 
10|-  times  5  ? 

27.  How  many  are  123-  times  7  ?  9|  times  10  ? 

28.  How  many  are  5|  times  15  ?  3^  times  40  ?    . 


84  INTELLECTUAL   ARITHMETIC.  [54, 

54.  1.  A  man,  owning  |  of  a  store,  sold  |  of 
his  share ;  what  part  of  the  whole  store  did  he 
sell? 

Analysts.  He  sold  \  of  ^-  of  the  store.  Smce  -J  ia 
equal  to  |,  \  of  ^  is  equal  to  \  of  ^^  or  |.  Therefore^ 
he  sold  ^  of  the  store. 

2.  James  had  |  of  a  dollar,  and  gave  |-  of  it  to  a 
beggar ;  what  part  of  a  dollar  did  he  give  away  ? 

8.  A  boy,  having  |  of  a  watermelon,  gave  away  J 
of  what  he  had  ;  Avhat  part  of  the  whole  melon  did 
he  give  away  ? 

4.  If  a  yard  of  crape  cost  |  of  a  dollar,  what  will 
■J  of  a  yard  cost  ? 

5.  If  I  own  ^  of  an  acre  of  land,  and  sell  J  of  it, 
what  part  of  an  acre  do  I  sell  ? 

6.  If  a  bushel  of  apples  be  worth  ^  of  a  dollar, 
what  is  J  of  a  bushel  worth  ? 

7.  John  is  ^  as  old  as  his  fatlier,  and  Henry  is  \ 
as  old  as  John  ?  what  part  of  his  father's  age  is 
Henry's  age  ? 

8.  A  merchant,  having  -J  of  a  hogshead  of  molas- 
ses, sold  J  of  what  he  had  ;  what  part  of  the  whole 
hogshead  did  he  sell,  and  what  part  had  he  left  ? 

9.  Homer  bought  ^  a  box  of  figs,  and  Robert  |- 
as  many  ;  Avhat  part  of  a  box  did  ])oth  buy  ? 

10.  C  owned  J  of  a  steamboat,  and  sold  ^  of  his 
share  ;  what  part  of  the  whole  did  he  sell  ? 

11.  Mr.  Jones,  owning  }^  of  a  cotton  mill,  sold  |- 
of  his  share  to  B,  and  B  "sold  ^  of  his  sliare  to  C  ; 
what  part  of  the  whole  did  each  have  after  the  di- 
vision ? 

12.  A  cistern,  being  full  of  water,  sprang  a  leak, 
and  before  it  could  be  stopped  |  of  the  water  ran 
out,  but  J  as  much  ran  in  at  the  same  time ;  what 
part  of  the  cistern  was  emptied  ? 

13.  A  poor  man,  having  I  of  a  barrel  of  flour. 


54.]  INTELLECTUAL   ARITHMETIC.  S5 

gave  l  of  it  to  a  poor  neighbor,  who  gave  ^  Oi  his 
share  to  a  poor  woman  ;  what  part  of  a  barrel  i^ad 
each  then  ? 

14.  Andrew,  having  8f ,  gave  |  of  it  for  a  knife  ; 
what  part  of  a  dollar  did  he  pay  for  his  knife  ? 

Analysis.  He  paid  ^  of  ^  of  a  dollar.  3  fifths  of  J 
are  3  times  1  fifth  of  ^.  ^  of  ^  is  ^^^,  and  ^  of  ^  are  3  times 
^u-5  or  ^^.      Therefore,  Sfc. 

15.  If  a  yard  of  cloth  is  worth  ^J,  what  is  J  of  a 
yard  worth  ? 

16.  Harriet,  having  |  of  a  yard  of  silk,  gave  |  of 
it  to  her  sister ;  what  part  of  a  yard  did  she  give 
away,  and  what  part  of  a  yard  had  she  left  ? 

17.  A  man,  owning  |-  of  a  farm.,  sold  |  of  his  share 
to  his  brother  ;  what  part  of  the  farm  did  eacli  own  ? 

18.  Hannah  picked  y^  of  a  pailful  of  strawberries, 
and  on  her  way  home  spilled  |  of  them ;  what  part 
of  a  pailful  had  she  left  V 

19.  What  will  be  the  cost  of  f  of  a  bushel  oi 
beans  at  8f  a  bushel  ? 

20.  Jacob,  having  |  of  a  pound  of  candy,  gave  ^- 
of  it  to  Mary,  and  ^  of  it  to  Jane ;  what  part  of  a 
pound  had  he  left  ? 

21.  A  keeper  of  a  saloon  bought  a  cask  of  ale  ;  | 
of  it  leaked  out,  |  of  the  remainder  he  sold,  and 
what  was  left  he  kept  for  his  own  use ;  what  part  of 
the  cask  did  he  keep  ? 

22.  How  do  you  multiply  one  fraction  by  another  2 

23.  What  is  1  of  1^  ?  29.    What  is  -J  of  i  ? 

24.  What  is  I  of  I-  ?  30.    What  is  i  of  i  ? 

25.  What  is  ^  of  I  ?  31.   What  is  i  of  J  ? 

26.  What  are  4  of  1?  32.    What  is  l  of  |  ? 

27.  What  are  |  of  |  ?  33.    What  are^^  of  |  ? 

28.  What  are  j  of  -fj  ?         34.    What  are  i  of  ^^^  ^ 


86  INTELLECTUAL   AEITHMETIC.  [55. 

55,  1.  At  $8|  a  barrel,  what  will  -|  of  a  barrel 
of  flour  cost  ? 

Analysis.  Since  1  barrel  cost  $8|,  |-  of  a  barrel,  which 
is  3  times  ^,  will  cost  3  times  ^  of  $8|-.  ^  of  $8  is  $2,  and 
1.  of$^  is  $1,  which  added  to  $2  makes  $2|.  3  ti?nes  $2 
H7e  $6.  and  3  times  -i-  are  f,  which  added  to  $6  wiaZ;e  $C|, 
Therefore^  ^-c. 

Or,  $8|-  are  e^z^aZ  to  -*^S  a?2c?  f  o/^-^^-  =  \3-,  or  $6f. 

2.  At  %^\  a  bushel,  what  will  |  of  a  bushel  of 
clover  seed  cost  ? 

3.  At  $12 1  a  ton,  what  will  |  of  a  ton  of  hay  cost  ? 

4.  If  a  man  travel  24J  miles  in  1  day,  how  far 
will  he  travel  in  \  of  a  day? 

5.  What  will  |  of  a  barrel  of  beef  cost,  at  $15 1  a 
barrel  ? 

6.  What  will  be  the  cost  of  \  of  a  cord  of  wood, 
if  1  cord  cost  %b\  ? 

7.  At  10|-  shillings  a  day,  how  much  can  a  man 
earn  in  |  of  a  day  ? 

8.  If  a  man  can  cut  3^-  acres  of  rye  in  1  day,  how 
much  can  ho  cut  in  |  of  a  day  ? 

9.  If  I  pay  $o|  for  ajar  of  butter,  what  is  \  of  it 
worth  ? 

10.  Bought  a  horse  for  $75|-,  and  sold  him  for  | 
of  what  he  cost ;  what  was  the  loss  ? 

11.  What  is  \  of  14H  of  20|?  of  13|?  of  ISJ? 

12.  What  are  |  of  9|  ?  of  12|  ?  of  16f  ?  of  2l|  ? 

13.  What  are  \  of  216-  ?  .a  of  32^  ?  f  of  23.5  ? 

14.  At  if  a  yard,  what  will  6-|-  yards  of  flannel 

iJOSt  ? 

Analysis.  Since  1  yard  costs  $f ,  6^  yards  will  cost  G^ 
times  $f .  6  tiriies  S|  are  J-^^.  ^,;.  ^4^  ^^^rtf  ^  o/"  f  z s  -/^-j  or 
^^,  which  added  to  $4  makes  $4^.      Therefore^  Sfc. 

Or,  61  are  egwaZ  to  ^^-,  aiid  y-  off  are  \^,  or  $4|^. 
Therefore,  S^c. 

15.  At  $1  a  bushel,  what  will  8|  bushels  of  peaches 
cost  ? 


55.]  INTELLECTUAL   ARITHMETIC.  87 

16.  If  a  man  hoe  ^  of  an  acre  of  corn  in  1  day, 
how  many  acres  can  he  hoe  in  5|  days  ? 

17.  If  a  vessel  sail  12 1  miles  in  1  hour,  how  far 
does  she  sail  in  |  of  an  hour  ? 

18.  If  a  man  has  22|  bushels  of  clover  seed,  and 
he  sell  I  of  it,  how  much  has  he  left  ? 

19.  What  will  -^  of  -|-  of  12  gallons  of  oil  cost,  at 
^A  a  gallon  ? 

20.  At  $^  a  rod,  what  will  it  cost  to  dig  I  of  f  of 
28  rods  of  ditch  ? 

21.  What  will  4|-  yards  of  cloth  cost  at  |2i  a 
yard  ? 

Note.     Reduce  the  mixed  numbers  to  improper  fractions,  and  then 
proceed  as  in  multiplying  one  fraction  by  another. 

22.  If  you  earn  8^  shillings  in  1  day,  how  much 
can  you  earn  in  2-|  days  ? 

23.  What  cost  2|  dozen  of  eggs  at  lOJ  cents  a 
dozen  ? 

24.  What  will  3f  yards  of  shalloon  cost  at  $1-^^ 
a  yard  ? 

25.  If  a  man  can  do  a  job  of  work  in  5|  days,  in 
what  time  can  he  do  a  job  1|  times  as  large  ? 

26.  Clorinda  is  7|  years  old,  and  Augusta  is  f  as 
old  ;  how  old  is  she  ? 

27.  A  man  paid  $16f  for  a  cow,  and  2|-  times  as 
much  for  a  colt ;  how  much  did  he  pay  for"  both  ? 

28.  What  is  the  product  of  3|  times  9^  ? 

29.  What  is  the  product  of  8^  times  lOf  ? 

30.  What  is  the  product  of  ^  of  f  of  16  multi- 
plied by  5f  ? 

31.  What  is  the  value  of  |  of  i  of  6|  ? 

32.  What  is  the  value  of  |  of  |  of  30  ? 

33.  What  is  the  value  of  |  of  |  of  I  ? 

34.  What  is  9j%  times  f  ?  4i  times  1^  ? 

35.  What  is  10^  times  2f  ?  2^  times  25J  ? 


88  INTELLECTUAL   ARITHMETIC.      •  [*56. 

56.  1.  If  S  pounds  of  raisins  cost  $|,  what  will 
1  pound  cost  ? 

Analysis.  If  3  pounds  cost  $|-,  1  pounds  which  is  ^ 
of  3  pounds,  will  cost  ^  of  $^,  or  $'f.      Therefore,  SfC. 

2.  If  4  slates  cost  $|,  what  will  1  slate  cost  ? 

3.  If  5  pounds  of  sugar  cost  ||,  what  will  1  pound 
cost  ? 

4.  If  3  oranges  are  worth  |  of  a  melon,  what  part 
of  the  melon  is  1  orange  worth  ? 

Note.  It  will  be  remembered  that  a  fraction  may  be  divided  by  a 
whole  number  either  by  dividiny  the  numerator  ov  multiplying  the  denom' 
inator  by  it.     (See  pages  72  and  73,  notes.) 

5.  If  6  pounds  of  coffee  cost  ||,  what  will  1  pound 
cost  ? 

6.  If  4  apples  cost  |-  of  a  shilling,  what  will  1 
apple  cost  ? 

7.  If  5  yards  of  sheeting  cost  ||,  what  will  1  yard 
cost  ? 

8.  If  4  figs  cost  I  of  a  dime,  what  will  1  fig  cost  ? 

9.  What  will  1   yard  of   linen   cost,  if  4  yards 

cost  ^  ? 

10.  Marcus  had  |  of  a  melon,  which  he  wished  to 
divide  equally  hetween  his  2  sisters ;  what  part  must 
he  give  to  each  ? 

11.  Oliver,  having  12  quarts  of  blueberries,  sold  | 
of  them  for  $|  ;  what  was  that  a  quart  ? 

12.  If  6  persons  agree  to  share  equally  |  of  a 
bushel  of  grapes,  what  part  of  a  bushel  will  each 
have  ? 

13.  If  you  divide  |  of  a  barrel  of  flour  among  3 
poor  families,  what  part  of  a  barrel  will  you  give  to 
c^ch  ? 

14.  How  many  times  is  7  contained  in  f  ?  5  in 
i^  ?  8  in  I-  ?  10  in  {^  ? 

15.  What  is  the  quotient  of  |f  divided  by  5  ?  by  7  ? 

16.  What  is  the  quotient  of  ^  divided  by  3  ?  by  4  ? 


57.]  INTELLECTUAL   ARITHMETIC.  8& 

57,  1.  At  8|  a  yard,  how  many  yards  of  silk 
can  be  bought  for  8<3  ? 

Analysis.  As  manij  yards  as  $|-,  the  price  of  1  ijardj 
is  contained  times  in  36  ;  30  is  equal  to  S*^^*,  and  S|-  is  con- 
tained in  $-^*-  8  times.  Tlierefore^  at  %^  a  yard,  8  yards  oj 
silk  can  he  bought  for  $6. 

2.  If  a  boy  can  earn  f  |  a  day,  how  long  will  it 
take  him  to  earn  $5  ? 

3.  How  long  will  it  take  a  man  to  spend  $10  for 
cigars,  if  he  spend  8]-  a  day  ? 

4.  When  potatoes  are  ti|  per  bushel,  how  many 
bushels  can  be  bought  for  88  ? 

5.  At  8 J  a  pair,  how  many  pairs  of  shoes  can  be 
bought  for  87  ? 

6.  How  much  butter  can  be  bought  for  83,  at  8 J 
a  pound  ? 

7.  How  many  times  is  4  contained  in  4  ?  in  7  T 
in  8  ? 

8.  If  the  cars  run  |  of  a  mile  a  minute,  how  long 
will  they  be  in  running  25  miles  ? 

9.  If  a  horse  eat  |^  of  a  bushel  of  pats  a  day,  how 
long  will  9  bu.shels  last  him  ? 

10.  If  a  man  walk  |  of  a  mile  in  ^  of  an  hour, 
how  long  will  it  take  him  to  walk  12  miles  ? 

11.  How  many  bushels  of  oats,  worth  85  a  bushel, 
will  pay  for  |  of  a  barrel  of  flour,  worth  89  a  barrel  ? 

12.  A  farmer  sold  a  grocer  1  ton  of  hay  for  812, 
and  received  ^  the  amount  in  sugar  at  8J  a  pound, 
^  in  money,  and  the  remainder  in  molasses  at  8?  a 
gallon ;  how  many  pounds  of  sugar,  and  how  many 
gallons  of  molasses,  did  he  receive  ? 

13.  If  1^  of  a  barrel  of  trout  cost  812,  what  will  1 
barrel  cost  ? 

14.  If  I  of  a  ton  of  hay  cost  87,  what  will  1  ton 
cost  ? 


90  INTELLECTUAL   ARITHMETIC.  [58, 

15.  "When  potatoes  arc  worth  $|  a  bushel,  and 
corn  $1  a  bushel,  how  many  bushels  of  potatoes  are 
equal  in  value  to  16  bushels  of  corn  ? 

16.  How  many  yards  of  ribbon,  at  |  of  a  shilling 
a  yard,  can  be  bought  for  7  shillings  ? 

17.  If  1  man  consume  |  of  a  pound  of  meat  in  a 
day,  how  many  men  would  6  pounds  supply  ? 

18.  If  I  of  a  hogshead  of  molasses  cost  $36,  what 
will  one  hogshead  cost  ? 

19.  If  I  of  an  acre  of  land  sell  for  $21,  what  will 
an  acre  sell  for  at  the  same  rate  ? 

20.  How  many  pounds  of  tea,  worth  $-^  a  pound, 
must  be  given  for  9  bushels  of  apjoles,  worth  $|  a 
bushel  ? 

21.  How  many  times  is  |-  contained  in  5  ?  in  7  ? 
in  9  ?  in  11  ?  in  15  ? 

22.  How  many  times  is  |  contained  in  12  ?  in  18  ? 
in  20  ?  in  15  ? 

23.  How  many  times  is  J  contained  in  |  ?  in  ||  ? 
in  II?  in  I? 

24.  How  many  times  is  J  contained  in  |  of  16  ? 
in  I  of  27  ? 

25.  How  is  a  whole  number  divided  by  a  fraction  ? 


58.  1.  At  $2  a  bushel,  how  many  bushels  of 
wheat  can  be  bought  for  fllj^  ? 

Analysis.  As  many  huskels  as  $2,  the  price  of  1  bushel^ 
is  contained  times  in  $11^.  11^  are  equal  to  4j^,  and  2  is 
contained  in  %*-,  J/-,  or  5f  times.      TJierefore,  S^c. 

Or,  2  is  contained  in  11^,  5  times,  and  \^  or  ^over  ;  and 
2  is  contained  in  ^,  f  times,  which  added  to  5  males  of 
times.     Therefore,  S)-c. 

2.  If  6  pounds  of  coffee  cost  $lf ,  what  is  the  cost 
of  1  pound  ? 


59.]  INTELLECTUAL    ARITHMETIC.  91 

3.  If  a  man  walk  18|-  miles  in  4  hours,  liow  many 
miles  does  he  walk  in  1  hour  ? 

4.  How  many  times  will  16|-  gallons  of  cider  fill  a 
vessel  that  holds  3  gallons  ? 

5.  How  many  oranges,  at  3  cents  apiece,  can  be 
bouQ'ht  for  -i  of  4  of  60  cents  ? 

6.  At  $4  a  yard,  how  many  yards  of  cloth  can  be 
bought  for  ^'lif  V 

7.  If  a  turkey  cost  T  shillings,  how  many  turkeys 
can  be  bought   for  38J  shillings  ? 

8.  At  5  shillings  a  gallon,  how  many  gallons  of 
molasses  can  be  bou2.-ht  for  244  shillina's '( 

9.  If  a  day  laborer  earn  88f  in  10  days,  how  much 
does  he  earn  in  1  day  ? 

10.  If  a  locomotive  run  4-|  miles  in  6  minutes, 
how  far  does  she  run  in  1  minute  ? 

11.  If  12  bushels  of  oats  cost  84-J,  what  part  of  a 
dollar  will  1  bushel  cost  ? 

12.  If  7  pounds  of  coffee  cost  84    dimes,    what 
will  1  pound  cost  ? 

13.  Divide  81  bv  5  ;  lOf  by  7  ;  15^  by  15. 

14.  Divide    9i  "by    7 ;    18.^  by    12 ;    20^    by  l 
of  16. 

15.  Divide  I  of   21  by  f  of  10.     |  of  29  by  ^ 
of  63. 


59.  1.  At  8|  a  pound,  how  many  pounds  of 
iea  can  be  bought  for  8f  'i 

Analysis.  As  many  pounds  as  $|,  the  price  of  1 
pound,  is  contained  times  in  Sf.  f  equal  ^^,  f  equal  ^, 
and  S  twentieths  are  contained  in  15  twentieths  \\  times. 
Therefore,  at  S|  a  pound,  \\  pounds  can  he  hought  for  $|. 

Or  thus  :  \  is  contained  in  1,  5  times,  and  in  ^  of  1  it  is 
contained  f  rf  5  times,  or  -^^-  times  ;  f  is  contained  in  |,  ^ 
as  many  times,  and  i  of  ^-f-  is  Jg^-,  or  1|. 


92  INTELLECTUAL   ARITHMETIC.  [*59. 

2.  How  many  pounds  of  honey,  at  $^  a  pound, 
can  be  bought  for  ^  J  ? 

3.  In  I  of  an  acre  of  land,  how  many  building 
lots  of  -^Q  of  an  acre  each  ? 

4.  If  a  horse  eat  -|  of  a  bushel  of  oats  in  a  day, 
in  how  many  days  will  he  eat  -^^  of  a  bushel  ? 

5.  At  f  of  a  cent  apiece,  how  many  slate  pencils 
can  be  bought  for  |  of  a  cent  ? 

6.  If  a  piece  of  ribbon  |  of  a  yard  long  be  cut 
Into  pieces  i  of  a  yard  in  length,  how  many  pieces 
will  there  be  ? 

7.  A  man,  owning  |  of  a  coal  mine,  divided  his 
share  equally  among  his  sons,  giving  them  ^^g  each ; 
how  many  sons  had  he  ? 

8.  Among  how  many  children  can  you  divide  -|  of 
If  melons,  if  you  give  |-  of  ^  of  a  melon  to  each  ? 

9.  At  $1  a  yard,  how  many  yards  of  silk  can  be 
bought  for  If  ? 

10.  At  I  of  |-  of  a  dollar  a  yard,  how  many  yards 
of  ribbon  can  be  bought  for  $^  ? 

11.  At  $X  a  pint,  how  much  wine  can  be  bought 
for  $1  ? 

12.  When  peaches  are  worth  8|  a  bushel,  how 
many  can  be  bought  for  $|  ? 

13.  If  I  of  a  yard  of  silk  cost  If,  what  will  1  yard 
cost  ? 

Analysts.  It  will  cost  3  times  ^  of  $f ,  or  f  of  $f .  ^ 
of  f  is  |,  a7id  3  times  |  are  f,  or  $1J-.  Therefore,  if  f  of 
a  yard  of  silk  cost  $|-,  1  yard  ivill  cost  $1|-. 

14.  What  will  1  dozen  eggs  cost,  if  |  of  a  dozen 
cost  I  of  a  dime  ? 

15.  If  I  of  a  bushel  of  corn  are  worth  ^^-  of  a 
bushel  of  rye,  how  many  bushels  of  corn  is  1  bushel 
of  rye  worth  ? 

16.  Horace  had  f|,  which  was  |^  of  what  he  paid 
for  a  cap ;  what  was  the  cost  of  his  cap  ? 


*59.]  INTELLECTUAL   ARITHMETIC.  93 

17.  If  I  of  a  yard  of  clotli  cost  $^-q,  what  will  1 
yard  cost  ? 

18.  James  bought  -|  of  a  pineapple,  which  was  |- 
of  Avhat  Luther  bought ;  what  part  of  a  pineapple 
did  Lutlier  buv  ? 

19.  If  I  of  a  drum  of  figs  cost  f  |,  what  will  1 
drum  cost  ? 

20.  How  many  times  can  a  bottle  holding  ^  of  |- 
of  a  gallon  be  filled  from  a  demijohn  containing  |-  of 
1-|  gallons  ? 

21.  Divide  |  by  |  ;  -^^  by  |- . 

22.  Divide  f|  by  |  ;  -^j  by  f. 

23.  Divide  f  by  }  ;  f  by  f . 

24.  Divide  ^-  of  f  by  f ;  |  of  |  by  l  of  f . 

25.  Divide  if  by  J-  of  f ;  ^  by  |. 

26.  Divide  e  by  i;3V  by  ^. 

27.  How  many  times  are  |  contained  in  -^-^  ? 

28.  How  many  times  are  f  contained  in  ^^g  ? 

29.  How  many  times  are  f  contained  in  ^  ? 

30.  How  many  times  are  -|  contained  in  |-i-  ? 

31.  How  many  times  are  |-  contained  in  |  ? 

32.  How  many  times  are  J  of  -|  contained  in  ^  ? 

33.  How  many  times  are  -J  contained  in  J  of  1-^  ? 
84.  How  many  times  are  J-  of  -|  contained  in  |-  of  |^  ? 

35.  "I  are  f  of  what  number  ? 

Analysis.     I  are  |  q/*4  times  i  of  ^  ;  I  of  ^  are  j^, 
a?ul  4  ^mes  /^  ci^e  ^f .     Therefore^  %  are  |  o/*  ^|. 

36.  1^  are  \  of  what  number  ? 

37.  -|  are  -|  of  what  number  ? 

38.  y^5  are  |  of  what  number  ? 

39.  \  are  f  of  what  number  ? 

40.  -^  are  \  of  what  number  ? 


94  INTELLECTUAL   ARITHMETIC.  [60. 

<S0.  1.  At  1|  dollars  a  yard,  how  many  yards  of 
cloth  can  be  bought  for  111  ? 

Analysis.  As  many  yards  as  $1|^,  tlie  price  of  1  yard, 
is  contained  times  in  $11.  $1|  are  $V;  $11  are  $^-^-, 
and  -\^  is  contained  in  ^^-,  G  times.  Therefore,  at  ^1|  a 
yard,  6  yards  of  cloth  can  be  bought  for  $11. 

2.  If  a  turkey  cost  $lf ,  how  many  can  be  bought 
for  J^9  ? 

3.  A  grocer  paid  |4|  for  some  onions,  at  the  rate 
of  ^1  a  bushel :  how  many  did  he  buy  ? 

4.  How  many  times  will  4|  gallons  of  camphene 
fill  a  vessel  that  holds  |  of  |  of  1  gallon  ? 

5.  If  4|  yards  of  velvet  ribbon  cost  I  J,  what  will 
1  yard  cost  ? 

6.  If  3|-  dozen  of  eggs  cost  $^'^,  what  is  the  cost 
of  1  dozen  ? 

7.  How  many  yards  of  flannel  worth  f|  a  yard 
can  be  bought  for  6  turkeys  worth  8|  apiece  ? 

8.  If  1  man  can  do  a  piece  of  work  in  6|  days,  in 
what  time  can  4  men  do  the  same  ? 

9.  If  a  man  chop  1^  cords  of  wood  in  a  day,  how 
long  will  it  take  him  to  chop  10  J  cords  ? 

Note.     Reduce  the  mixed  numbers  to  improper  fractions,  and  then 
divide  the  same  as  you  divide  one  fraction  by  another. 

10.  If  ^  baskets  of  peaches  are  worth  $3|,  what 
is  1  basket  worth  ? 

11.  If  51  bushels  of  apples  cost  81|,  what  is  the 
cost  of  1  bushel  ? 

12.  If  a  man  spend  $lf  a  month  for  tobacco,  in 
what  time  will  he  spend  $101  for  the  same  purpose  ? 

13.  At  41  shillings  a  gallon,  how  many  gallons  of 
molasses  can  be  bought  for  9|  shillings  ? 

14.  If  a  stage  run  24|  miles  in  3^  hours,  how  far 
does  it  run  in  1  hour  ? 

15.  Mr.  B.  distributed  l^  bushels  of  corn  equally 


60.]  INTELLECTUAL   ARITHMETIC.                          95 

among  some  poor  persons,  giving  them  1|  bushels 
each  ;  among  how  many  persons  did  he  divide  it  ? 

16.  Bought  1  of  71  cords  of  Avood  for  J  of  |32 ; 
w^hat  did  1  cord  cost  ? 

17.  A  father  divided  11 3^  acres  of  land  amoni!;  hi3  3 
sons ;  to  the  first  he  gave  |  of  it,  and  the  remainder  he 
divided  equally  between  the  other  2 ;  how  many  acrea 
did  each  receive  ? 

18.  Divide  91  by  6  ;  lOJ  by  7  ;  12|  by  31. 

19.  Divide  101-  by  |  ;  14  J  by  f  ;  201  by  |. 

20.  Divide  71  by  3| ;  15|  by  2|  ;  8|  by  5J-. 

21.  Divide  161  by  31 ;  20i-  by  1^^^  ;  Hi  b>  4f . 

22.  Divide  |  of  i  of  14  by  |  of  31 

23.  -|  are  how  many  times      6  ? 

24.  -^j  are  how  many  times      4  ? 

25.  ^1  are  how  many  times    15  ? 

26.  1^  are  how  many  times    6^  ? 

27.  12  are  how  many  times      |  ? 

28.  16  are  how  many  times      |-  ? 

29.  25  are  how  many  times      ^  ? 

30.  14  are  how  many  times    -f^  ? 

31.  14f  are  how  many  times      |  ? 
32i  6 1  are  how  many  times      |-  ? 

33.  21^  are  how  many  times      5  ? 

34.  32-|  are  how  many  times      7  ? 

35.  17 1  are  how  many  times      8  ? 

36.  15  are  how  many  times    7-J  ? 

37.  ISf  are  how  many  times    2^  ? 

38.  221  are  how  many  times    3|  ? 

39.  4:^Q  are  how  many  times    6|  ? 

40.  7f  are  how  many  times    4^  ? 

41.  8|  are  how  many  times    3|  ? 


96  INTELLECTUAL   ARITHMETIC.  [61. 

Gt.     1.   What  is  1  of  3  ? 

AvALTSTS.  That  number  lohich^  taken  4  times,  will 
make  3.  Since  1  fourtJi  of  1  is  ^,1  fourth  of  3  is  3 
ti?nes  I  of  1,  or  ^  of  1.    Therefore  |  o/3  is  |  ofl,  or^. 

2.  What  is  -1  of  3  ?  of  4  ?  of    6  ?  of    T  ? 

3.  What  is  -J  of  7  ?  of  3  ?  of    9  ?  of  15  ? 

4.  What  is  1  of  2  ?  of  4  ?  of    5  ?  of  11  ? 

5.  What  is  J  of  3  ?  of  5  ?  of    7  ?  of  13  ? 

6.  What  is  I  of  2  ?  of  3  ?  of    5  ?  of    7  ? 

7.  What  is  i  of  3  ?  of  5  ?  of    9  ?  of  14  ? 

8.  What  is  -}  of  4  ?  of  6  ?  of  12  ?  of  18  ? 

9.  What  is  l  of  5  ?  of  3  ?  of  20  ?  of  30  ? 

10.  What  is  -jV  of  7  ?  of  9  ?  of  16  ?  of  47  ? 

11.  AVhat  is  j\  of  4  ?  of  7  ?  of  11  ?  of  63  ? 

12.  What  is  -^\j  of   2  ?  of  7  ?  of  11  ?  of  34  ?  of  75  ? 

13.  What  is  2V  of  13  ?  of  9  ?  of  17  ?  of  50  ?  of  91  ? 

14.  If  5  bushels  of  wheat  cost  $9,  what  will  1 
bushel  cost  ? 

An-alysts.  If  5  bushels  cost  $9,  1  bushel,  which  is  1 
of  5  bushels,  will  cost  i  0/  |9  ;  i  0/  $9  is  $14.  There- 
fore, if  5  bushels  cost  $9,  1  bushel  will  cost  Si  J. 

15.  If  6  turkeys  are  worth  $5,  what  are  they 
worth  apiece  ? 

16.  If  you  divide  6  oranges  equally  among  7  boys, 
what  part  of  an  orange  will  each  receive  ? 

17.  If  a  man  travel  29  miles  in  9  hours,  how  far 
does  he  travel  in  1  hour  ? 

18.  If  1  man  can  build  a  barn  in  20  days,  in  what 
time  can  3  men  build  it  ? 

19.  If  a  horse  eat  5  bushels  of  oats  in  8  days, 
what  part  of  a  bushel  does  he  eat  in  1  day  ? 

20.  What  will  1  hat  cost,  if  4  hats  cost  $17  ? 


6S.]  INTELLECTUAL  ARITHMETIC.  97 

63.     1.   What  are  |  of  3  ? 

AxALYsis.  i  of  S  are  3  times  ^  o/  3  ;  |  o/  3  is  | 
of  1,  and  3  times  |  are  |  or  2|.  Therefore^  i  of  ^ 
ere  2i.  * 

2.  What  are  I  of  5  ?  of  4  ?  of    7  ? 

3.  What  are  f  of  4  ?  of  6  ?  of    8  ? 

4.  What  are   |  of  2  ?  of  3  ?  of    9  ?            > 
6.  What  are  |  of  3  ?  of  5  ?  of  10  ?  of  12  ? 

6.  What  are  -^^  of  4  ?  of    7  ?  of  15  ?  of  18  ? 

7.  What  are   |  of  2  ?  of    3  ?  of  14  ?  of  20  ? 

8.  What  are  |  of  5  ?  of    8  ?  of  19  ?  of  28  ? 

9.  What  are  i\  of  7  ?  of  13  ?  of  21  ?  of  30  ? 

10.  What  are  f  of    2  ?  of    6  ?  of  15  ?  of  24  ? 

11.  What  are  -^V  of    7  ?  of  36  ?  of  50  ?  of  63  ? 

12.  AVhat  are  -^^  of  35  ?  of  60  ?  of  77  ?  of  91  ? 

13.  What  are  o^  of  10  ?  of  15  ?  of  120  ?  of  150 1 

14.  If  4  cords  of  wood  cost  $14,  what  will  5  cord3 
cost  ? 

Analysis.  If  4  cords  of  loood  cost  $14,  5  co?'cZi? 
will  cost  5  ^rmes  ;i  o/|14.  \  o/$14  zs  $3^,  and  5  ^jmea 
$3 A  are  $17A.  Therefore  5  corc^s  <?/  i(;c»oc?  wiY^  cc»5^ 
$17  A. 

15.  If  3  bushels  of  quinces  cost  $7,  what  will  2 
bushels  cost  ? 

16.  If  9  bushels  of  apples  cost  $4,  what  will  7 
bushels  cost  ? 

17.  At  6  cents  for  2  oranges,  how  many  oranges 
could  you  buy  for  21  cents  ? 

18.  If  4  men  can  do  a  piece  of  work  in  15  days, 
in  what  time  can  6  men  do  the  same  ? 

19.  If  a  quantity  of  provision  will  last  5  men  9 
days,  how  long  would  the  same  last  11  men  ? 

7 


98  INTELLECTUAL   ARITHMETIC.  [63. 

63.  1.  If  1  pound  of  butter  cost  19  cents,  what 
will  I  of  a  pound  cost  ? 

2.  A  barrel  of  beer  sold  for  $S ;  what  was  |  of  it 
worth  ?         ♦  ^  . 

3.  Sold  a  cow  for  $18,  which  was  only  |  of  her 
real  value  ;  what  was  her  real  value  ? 

4.  Bought  a  carriage  for  $65,  and  afterwards 
sold  it  for  f  of  what  it  cost  me ;  how  much  did  I 
gain  ? 

5.  A  farmer,  having  80  sheep,  sold  ^  of  them  ; 
how  many  had  he  left  ? 

6.  If  I  give  4  pounds  of  butter,  worth  12  J  cents  a 
pound,  for  8  pounds  of  sugar,  what  is  the  sugar 
worth  a  pound  ? 

7.  After  paying  |  of  my  money  for  a  piece  of 
land,  I  had  |48  left ;  how  much  money  had  I  at 
first  ? 

8.  A  man  bought  a  watch  and  chain  for  $50, 
which  was  J  of  what  the  watch  alone  cost ;  what  was 
the  cost  of  each  ? 

9.  If  a  man  can  cut  9  cords  of  wood  in  |-  of  a 
week,  how  many  cords  can  he  cut  in  4  weeks  ? 

10.  A  man  paid- $35  for  a  book-case,  f  of  the 
cost  of  his  book-case  was  ^  of  what  he  paid  for  a 
bureau,  and  f  the  cost  of  the  bureau  was  ^  of  what 
he  paid  for  a  table  ;  what  did  he  pay  for  the  bureau, 
and  for  the  table  ? 

11.  If  4  quarts  of  chestnuts  cost  37  cents,  what 
will  1  bushel  cost  ? 

12.  If  a  man  can  walk  7  miles  in  2  hours,  how 
far  can  he  walk  in  3  days,  by  walking  10  hours  a 
day? 

13.  If  I  of  a  barrel  of  flour  is  worth  $8,  what  are 
12  barrels  worth  ? 

14.  If  3  pecks  of  grass-seed  cost  14  shillings, 
what  will  4  quarts  cost  ? 


63.]  INTELLECTUAL   ARITHMETIC.  99 

15.  If  3  yards  of  silk  cost  ^19-|-,  what  will  7  yards 
cost  ? 

16.  If  a  man  earn  832  J  in  1  weeks,  how  much  will 
he  earn  in  2  weeks  ? 

17.  If  $d  will  buy  4|-  yards  of  cloth,  how  much 
will  81  buy  ? 

18.  A  man,  having  56|  acres  of  land,  sold  |  of  it ; 
how  many  acres  did  he  sell  ? 

19.  If  9  horses  eat  5|  bushels  of  oats  in  a  day, 
how  many  bushels  will  1  liorses  eat  in  the  same  time  ? 

20.  If  3  yards  of  flannel  cost  8|,  what  will  8 
yards  cost  ? 

21.  If  10  bushels  of  wheat  are  worth  22|-  bushels 
of  corn,  how  many  bushels  of  corn  are  3  bushels  of 
wheat  worth  ? 

22.  If  11  acres  of  meadow  land  produce  32|  tons 
of  hay,  how  many  tons  will  5  acres  of  the  same  land 
produce  ? 

23.  A  cistern  is  filled  by  3  pipes  in  6|  hours  ;  how 
many  pipes  of  the  same  size  will  be  required  to  fill  it 
in  ^  of  an  hour  ? 

24.  A  boy  sold  5  quarts  of  strawberries  at  the  rate 
of  3  quarts  for  13  cents  ;  how  much  did  he  receive 
for  the  whole  ? 

25.  A  tailor  bought  3  pieces  of  cassimere,  each 
piece  containing  6|  yards,  for  8484  ;  how  much  did 
it  cost  a  piece,  and  how  much  a  yard  ? 

26.  If  a  pole  8  feet  long  cast  a  shadow  6  feet,  how 
long  is  a  pole  that  casts  a  shadow  12|-  feet  at  the 
same  time  ? 

27.  How  much  less  than  817  will  9  yards  of  satin 
cost,  if  2  yards  cost  83^  ? 

28.  If  3  yards  of  velvet  cost  $b^,  how  much  more 
than  89  will  6  yards  of  it  cost  ? 

29.  If  a  horse  travel  40|-  miles  in  6  hours,  how 
far  will  he  travel  in  4  hours  ? 


100  INTELLECTUAL   ARITHMETIC.  [04, 

64.  1.  If  5  pounds  of  chalk  cost  2 8 J  cents, 
what  will  I  of  a  pound  cost? 

2.  If  3  pairs  of  socks  cost  |^^,  how  many  pairs 
can  be  bought  for  ^2-^^  ? 

3.  Lucas  is  f  as  old  as  his  father,  who  is  60  years 
of  age  ;  what  is  Lucas's  age  ? 

4.  If  I  of  a  box  of  raisins  cost  $2-^.j,  what  will  | 
of  a  box  cost  ? 

5.  A  boy  sold  some  peaches  for  6|  cents,'  at  the 
rate  of  3  for  4|  cents  ;  how  many  did  he  sell  ? 

6.  If  7  bushels  of  oats  cost  5^1|,  what  will  12| 
bushels  cost  ? 

7.  If  2 1  yards  of  shalloon  cost  $4|,  what  will  5 
yards  cost? 

8.  Bought  4|^  barrels  of  cider  at  i3|  a  barrel,  and 
paid  in  wood  at  i3  a  cord ;  how  many  cords  of  wood 
paid  for  the  cider  ? 

9.  John  has  $5-J,  and  Gilbert  has  1|  times  as 
much  ;  how  much  has  Gilbert  ? 

10.  Three  men  incur  an  expense  of  $27|  ;  how 
much  more  than  $7|  must  each  pay  ? 

11.  A  man,  being  asked  his  age,  said  that,  were  he 
3  times  as  old,  -f^  of  his  age  would  be  8  years ;  how 
old  was  he  ? 

12.  If  a  pound  of  tea  is  worth  3 J  times  as  much 
as  a  pound  of  coffee,  what  will  6|  pounds  of  coffee 
cost,  when  tea  is  worth  50  cents  a  pound  ? 

13.  If  2|  pounds  of  cheese  cost  20  cents,  what 
will  12  pounds  cost  ? 

14.  If  31  barrels  of  apples  cost  |5|,  what  will  -| 
barrel  cost : 

15.  A  stone  mason  worked  llf  days,  and  after 
paying  his  board  and  other  expenses  with  |  of  his 
earnings,  had  $20  left ;  how  much  did  he  receive  a 
day? 


64.]  INTELLECTUAL   ARITHMETIC.  101 

16.  If  7  bushels  of  potatoes  cost  $3|-,  how  many 
bushels  can  be  bought  for  $14:}  ? 

IT.  If  -|-  of  a  quart  of  brandy  cost  875  how  many 
gallons  will  81 2|-  buy  ? 

18.  How  many  yards  of  silk  can  be  bought  for  30 
shillings,  if  3  shillings  be  paid  for  |  of  a  yard  ? 

19.  If  I  of  a  shilling  Avill  buy  |-  of  a  pound  of 
butter,  how  many  pounds  will  7  shillings  buy  ? 

20.  How  many  gallons  of  molasses  can  be  bought 
for  83-|^,  if  ^  of  a  gallon  cost  8  J-  ? 

21.  How  many  oats  can  be  bought  for  10  shillings, 
if  9  bushels  cost  24  shillings  ? 

22.  If  5  dozen  of  eggs  cost  4|  shillings,  how  many 
dozen  can  be  bought  for  7  shillings  ? 

23.  If  8  yards  of  velvet  ribbon  cost  81-^,  how  many 
yards  can  be  bought  for  83-^-  ? 

24.  How  many  pints  of  alcohol  will  3  shillings 
buy,  if  J  of  a  pint  cost  ^  of  a  shilling  ? 

25.  If  a  man  eat  1|-  pounds  of  bread  in  a  day,  how 
many  days  will  22^  pounds  last  him  ? 

26.  How  many  pounds  of  sugar  worth  10  cents  a 
pound  can  be  had  for  6f  pounds  of  cheese  worth  7^ 
cents  a  pound  ? 

27.  If  a  horse  consume  8-|-  bushels  of  oats  in  3 
weeks,  how  many  bushels  would  he  consume  in  5 
weeks  ? 

28.  A  man  gave  6f  pounds  of  butter  at  12  cents 
a  pound  for  |-  of  a  gallon  of  oil ;  what  was  the  oil 
worth  a  gallon  ? 

29.  When  4  pounds  of  tea  can  be  bought  for  82|- , 
how  much  can  be  bought  for  Sy^  ? 

30.  A  man,  having  810,  gave  |  of  his  money  fop 
clover  seed  at  83|^  a  bushel ;  how  much  did  he  buy  ? 

31.  If  I  of  a  bushel  of  rye  cost  81-,  liow  many 
bushels  can  be  bought  for  87  ? 


102  INTELLECTUAL   ARITHMETIC.  [^5, 

<!l«l.  1.  If  |-  a  yard  of  cloth  cost  ||,  what  will  | 
of  a  yard  cost  ? 

2.  If  I  of  2  pounds  of  tea  cost  $1^,  what  will  |- 
of  1  pound  cost? 

3.  What  will  |  of  a  barrel  of  apples  cost,  if  |  of 
a  barrel  cost  ^|  ? 

4.  If  -|  of  a  pound  of  butter  is  worth  |-  of  a  pound 
of  fish,  how  many  pounds  of  fish  are  1|-  pounds  of 
butter  worth  ? 

5.  What  will  be  the  cost  of  G  barrels  of  flour  at 
the  rate  of  $2 1  for  every  |  of  a  barrel  ? 

6.  At  $J  a  quart,  what  part  of  a  bushel  of  clover 
seed  can  be  bought  for  |3-^-  ? 

7.  Since  I  was  25  years  old,  -|  of  my  entire  age 
has  passed  ;  what  is  my  age  ? 

8.  A  man,  engaging  in  play,  lost  ^  of  his  money, 
after  which  he  gained  $75,  when  he  found  that  he 
had  $375  ;  how  much  money  did  he  lose  ? 

9.  If  4  horses  consume  2|-  bushels  of  oats  in  2| 
days,  how  many  bushels  will  6  horses  consume  in 
the  same  time  ? 

10.  If  I  of  a  bushel  of  barley  be  given  for  |^  of  a 
bushel  of  corn  worth  $|  a  bushel,  what  is  the  barley 
worth  a  bushel  ? 

11.  A  person  having  a  drove  of  turkeys,  after  sell- 
ing 35,  found  that  he  had  -|  of  his  drove  left ;  how 
many  turkeys  in  his  drove  at  first  ? 

12.  What  number  is  that  to  which  if  |  of  itself 
be  added,  the  number  will  be  55  ? 

13.  What  number  added  to  3  times  -|  of  27  will 
make  the  number  40  ? 

14.  If  24  is  I  of  some  number,  what  is  i  of  the 
same  number  ? 

15.  What  number  taken  from  2|-  times  12|  will 
leave  20f  ? 


6^.]  INTELLECTUAL   ARITHMETIC.  103 

16.  If  140  exceed  by  |10,  i  of  f  of  what  I  gained 
in  the  sale  of  a  house  and  lot,  how  much  did  I  gain  ? 

17.  If  I  of  4  tons  of  coal  cost  $d^,  what  will  |  of 
2  tons  cost? 

18.  A  young  lady,  being  asked  her  age,  replied 
that  5  times  ^  of  30  years  was  4|-  years  more  than  3 
times  her  age  ;  what  was  her  age  ? 

19.  In  an  orchard,  |  the  trees  bear  apples,  4  bear 
peaches,  -^.j  bear  pears  and  15  trees  bear  plums ; 
how  many  trees  in  the  orchard,  and  how  many  of 
each  kind  ? 

20.  How  many  3^ards  of  cloth  that  is  |-  of  a  yard 
wide  are  equal  to  12  yards  |  of  a  yard  wide  ? 

21.  A,  B,  and  C  can  do  a  piece  of  work  in  5  days  ; 
B  and  C  can  do  it  in  8  davs ;  in  what  time  can  A  do 
it  alone  ? 

22.  A  can  build  a  piece  of  wall  in  3  days,  and  B 
can  build  it  in  4  days ;  in  what  time  can  both  build 
it  together  ? 

23.  If  I  the  value  of  a  carriage  is  equal  to  f  the 
value  of  a  horse,  and  the  difference  in  their  values  is 
$25,  what  is  the  value  of  each  ? 

24.  A  tailor  paid  873,  which  was  -^  of  all  the 
money  he  had,  for  cloth,  at  the  rate  of  f3  a  yard; 
how  many  yards  could  he  have  purchased  with  all 
his  money,  at  the  same  rate  ? 

25.  A  father  divided  a  piece  of  land  among  his  3 
sons  ;  to  the  first  he  gave  10|^  acres,  to  the  second  | 
of  the  whole,  and  to  the  third  as  much  as  to  the 
other  two  ;  how  many  acres  had  each  ? 

26.  A  farmer  bought  2  cows  for  $56,  paying  J  as 
much  for  one  as  for  the  other ;  how  much  did  each 
cost  him  ? 

27.  A  and  B  can  do  a  piece  of  work  in  14  days ; 
A  can  do  |  as  much  as  B ;  in  how  m^ny  days  can 
each  do  it  ? 


104  INTELLECTUAL   ARITHMETIC.  [66. 

66.     1.   16  is  I  of  what  number  ? 

Analysts.  16  is  i  of  5  times  ^  of  16  ;  ^  of  16  is  4^ 
and  5  times  4  are  20.     Therefore,  16  is  i  of  20. 

Or  thus:  Since  16  is  -|  of  some  number,  i  of  the  number, 
ivhich  is  i  of  \,  is  I  of  16,  or  4 ;  and  4  is  \  of  b  times  4j 
or  20.      Therefore,  ^c.    ^  ' 

2.  42  is  |-  .of  what  number  ? 

3.  25  is  f  of  what  number  ? 

4.  16  is  |-  of  what  number  ? 

5.  82  is  f  of  what  number  ? 

6.  60  is  -^j  of  what  number  ? 

7.  14  is  ^  of  what  number  ? 

8.  48  is  |-  of  what  number  ? 

9.  75  is  f  of  what  number  ? 

10.  84    is  1^1  of  what  number  ? 

11.  55    is  |-J  of  what  number  ? 


12. 

64 

is 

t'^ 

of  what  number  ? 

13. 

13 

is 

_a 

2 

of  what  number  ? 

14. 

18 

is 

5 
6 

of  what  number  ? 

15. 

28 

is 

of  what  number  ? 

16. 

40 

is 

1 

of  what  number  ? 

17. 

54 

is 

A 

of  what  number  ? 

18. 

10 

is 

A 

of  what  number  ? 

19.  12|-  is  ^  of  what  number  ? 

20.  15|  is  f  of  what  number  ? 

21.  19 1  is  ^  of  what  number  ? 

22.  241  is  -^j  of  what  number  ? 

23.  16|-  is  |-  of  what  number  ? 

24.  1^  is  f  of  what  number  ? 

25.  |-  is  f  of  what  number  ? 

26.  -^  is  f  of  what  number  ? 


2. 

18 

3. 

25 

4. 

36 

5. 

28 

6. 

40 

7. 

75 

67.]  INTELLECTUAL   ARITHMETIC.  105 

67.     1.    24  is  |-  of  how  many  times  10  ?  * 

Analysis.  24  is  |  of  as  7nany  times  10  as  10  is  coii- 
tained  times  in  5  tim,es  ^  of  24  ]  \  of  24:  is  6,  and  5 
iimes  Q  is  30;  10  is  contained  in  30,  3  times.  There- 
fore 24:  is  ^  of  Z  times  10. 

is  I  of  how  many  times  6  ? 
is  I  of  how  many  times  15  ? 
is  f  of  how  many  times  4  ? 
is  y^  of  how  many  times  8  ? 
is  -^.j  of  how  many  times  16  ? 
is  ^  of  how  many  times  20  ? 

8.  64    is  -|  of  how  many  times  24  ? 

9.  48    is  II  of  how  many  times  |-  of  30  ? 

10.  35    is  :|  of  how  many  times  -J-  of  28  ? 

11.  42    is  y^Y  of  how  many  times  \  of  63  ? 

12.  84    is  -y-  of  how  many  times  \  of  35  ? 

13.  27    is  3^g  of  how  many  times  J  of  72  ? 

14.  36    is  |-  of  how  many  times  ^  of  21  ? 

15.  14|  is  |-  of  how  many  times  ^  of  20  ? 

16.  16 1  is  1^  of  how  many  times  i  of  54  ? 

17.  12|-  is  -^^  of  how  many  times  -J-  of  40  ? 

18.  |-  is  |-  of  how  many  times  \  of    ^  ? 

19.  |-  of  f  is  f  of  how  many  times  |-  of  15  ? 

20.  James  gave  56  cents  for  a  pair  of  skates,  which 
was  I  of  what  he  gave  for  his  sled ;  wliat  did  his 
sled  cost  him  ? 

21.  A  farmer  paid  8231  for  a  cow,  which  was  \ 
of  what  he  received  for  a  horse  ;  what  was  the  dit- 
ference  in  the  price  of  the  cow  and  the  horse  ? 

22.  A  man  sold  4|-  cords  of  wood  at  82J  a  cord, 
which  was  |  of  what  he  received  for  a  ton  of  hay ; 
how  much  did  he  receive  for  the  hay  ? 

♦  Plea««  turn  to  67  in  the  Appendix,  page  170. 


106  INTELLECTUAL   ARITHMETIC.  [@8, 

23.  Paid  8 J  for  a  cravat,  which  was  |  of  what  I 
paid  for  a  vest ;  what  was  the  cost  of  the  vest  ? 

24.  A  gentleman  bought  a  sleigh  for  i50,  which 
was  I  of  o  times  what  he  paid  for  a  harness  ;  what 
did  the  harness  cost  him  ? 

25.  A  lady  bought  a  fur  cape  for  $90,  which  was 
■2^  of  what  she  paid  for  12  yards  of  silk  ;  what  was 
the  cost  of  the  silk  a  yard  ? 

26.  A  merchant  sold  5  barrels  of  flour  for  f  32|^, 
which  was  |  of  what  he  received  for  all  he  had  left, 
at  $4  a  barrel ;  how  many  barrels  in  all  did  he  sell  ? 


©8,     1.   I  of  20  is  how  many  thirds  of  24  ? 

Analysis,  i  of  20  is  as  many  thirds  of  24  as  \  of 
24  is  containecl  times  in  4  times  \  of  2^.  \  of  20  is  4, 
mid  4  times  4  ?'5  16  ;  8  is  contained  in  16,  2  times. 
Therefore,  f  of  20  is  |  of  24. 

2.  I  of    bQ  is  how  many  fourths  of  28  ? 

3.  f  of    64  is  how  many  fifths  of  60  ? 

4.  ^  of    48  is  how  many  sevenths  of  28  ? 
6.  "I  of  108  is  how  many  fourths  of  32  ? 

6.  ^^  of    90  is  how  many  twelfths  of  84  ? 

7.  /o  of  160  is  how  many  thirds  of  36  ? 

8.  -^y\  of  100  is  how  many  fifteenths  of  30  ? 

9.  I  of  lOf  is  how  many  sixths  of  12  ? 

10.  -J  of  37f  is  how  many  tenths  of  40  ? 

11.  I  of  42f  is  how  many  ninths  of  72  ? 

12.  I  of  78|  is  how  many  thirds  of  9  ? 

13.  f  of  28|-  is  how  many  halves  of  38  ? 

14.  i|  of    42  is  how  many  fourths  of  44  ? 

15.  ^9^  of    96  is  how  many  fifths  of  90  ? 

16.  J^gi  of    40  is  how  many  ninths  of  72  ? 


4 
69.]  INTELLECTUAL   ARITHMETIC.  107 

69.     1.   |-  of  24  is  I  of  what  number  ? 

Analysts.  -J  o/"  24  is  |  o/*  3  ^wi^-s  ^  o/'  5  ^?mes  J  of 
24  ;  Jo/*  24  is  4, '5  ^/w?<?.9  4  is  20  ;  ^  o/*  20  is  10,  a?zc?  3 
^/;72es  10  is  30.     T/icrefore  |  o/  24  i^s  |  o/  30. 

2.  f  of    56  is  ^-"^  of  what  number  ? 

3.  ^4j  of    88  is   |-   of  what  number  ? 

4.  -|  of    36  is  y^g-  of  what  number  ? 

5.  f  of    27  is   |-    of  what  number  ? 

6.  -^^  of    60  is  TT  of  what  number  ? 

1  o  1  o 

7.  f  of    52  is    I   of  what  number  ? 

8.  -^  of    81  is  -^Q  of  what  number  ? 

9.  |-  of    63  is   |-   of  what  number  ? 

10.  I  of  100  is  ll  of  what  number  ? 

11.  -j^g  of    96  is  -fj  of  what  number  ? 

12.  I  of  f  of  64  is   f   of  what  number  ? 

13.  I  of  -J-  of  75  is  i^  of  what  number  ? 

14.  1^  of  |-  of  56  is   |-   of  f  of  what  number  ? 

15.  -|  of  ^  of  72  is  i   of  f  of  what  number  ? 

16.  1^  of  I  of  36  is    I   of  -|-  of  what  number  ? 

17.  f  of  35  is  I  of  how  many  times  7  ? 

AxALTSis.  I  of  35  is  I  of  as  many  times  7  as  ^  is 
contained  times  in  8  times  \  of  3  times  ^  of  35  ;  ^  of 
35  is  5^  and  3  ^i??zes  5  ^s  15  ;  |  o/ 15  ^s  3,  «7zc/  8  times  3  ?> 
24  ;  7  is  contained  in  24  3|  times.  Therefore^  |-  o/"  35 
is  f  o/'3|  times  7. 

18.  "I  of  54  is   |-   of  how  many  times  5  ? 

19.  f  of  24  is  -^-^  of  how  many  times  12  ? 

20.  I  of  75  is  -^  of  how  many  times  8  ? 
of  56  is   |-   of  how  many  times  20  ? 


91  4 


"V 


22.     I  of  108  is   -\   of  how  many  times    9  ? 


ft 


108  INTELLECTUAL  ARITHMETIC.  [70. 

23.  -^j  of  121  are  |  of  how  many  times  7  ? 

24.  1^  of    33  are  -J  of  how  many  times  6  ? 

25.  II  of    34  are  f  of  how  many  times  14  ? 

26.  |-  of    30  are  |-|  of  how  many  times  20  ? 

27.  I  of  ^  of  63  are  ^  of  |  of  how  many  times  11  ? 

28.  I  of  I  of  50  are  J  of  J  of  how  many  times  8  ? 


70.     1.   ^-  of  56  are  |-  of  3  times  what  number  ?  * 

Analysis.  4  0/  56  are  |  0/  3  times  i  of  9  times  | 
of  4  times  ^  of  B6  ;  4  of  5Q  is  8,  and  4  ^zmes  8  z5  32  ; 
^0/32  is  4,  and  9  times  4  is  36  ;  j  o/36  es  12.  ^^a^e- 
/ore,  4  <y  56  «^<2  f  ^/*  3  ^me5  12. 

2.  |-  of   45  are  |-  of    6  times  what  number  ? 

3.  f  of    64  are  ^  of    9  times  what  number  ? 

4.  |-  of    63  are  j%  of    4  times  what  number  ? 

5.  |-  of    36  are  -^q  of    5  times  what  number  ? 

6.  -j^  of  110  are  |-  of    8  times  what  number  ? 

7.  IJ  of    80  are  -|  of  11  times  what  number  ? 

8.  |-  of    72  are  -f-^  of    5  times  what  number  ? 

9.  I  of    81  are  ||  of  10  times  what  number  ? 

10.  J  of    21  are  ^  of    8  times  what  number  ? 

11.  f  of    14  are  f   of    3  times  what  number  ? 

12.  I  of  f  of  70  are  -5^2"  of  4  times  what  number  ? 

13.  A  man,  being  asked  his  age,  answered  that  if 
he  were  3  times  as  old,  |  of  his  age  would  be  24 
years ;   how  old  was  he  ? 

14.  A  gentleman  divided  his  farm  between  his  2 
sons,  giving  the  elder  10  acres  more  than  |  of  the 
whole,  and  the  younger  the  remainder,  which  was  22 
acres  more  than  J  of  the  whole ;  how  many  acres  in 
the  farm  ? 

*  See  70  in  the  Appendix,  page  170. 


70.]  INTELLECTUAL   ARITHMETIC.  109 

15.  A  coal  merchant  sold  |  of  what  coal  he  had 
on  hand  for  ^90,  at  the  rate  of  ^6  a  ton  ;  how  many 
tons  had  he  ? 

16.  Bouglit  a  piano  for  8300,  and  |  of  the  cost  of 
the  mstriiment  was  |  of  what  I  received  of  9  young 
ladies  for  its  use  one  year ;  how  much  did  each 
young  lady  pay  for  its  use  ? 

17.  The  tools  in  a  shop  are  worth  $80  ;  |  of  this 
is  I  of  I  of  2  times  the  value  of  the  stock  ;  what  is 
the  value  of  the  stock  ? 

18.  A  peddler,  after  selling  8200  worth  of  his  stock 
in  trade,  finds  that  |  of  the  remainder  is  equal  to  | 
of  3  times  the  amount  sold ;  what  amount  of  stock 
had  he  at  first  ? 

19.  A  merchant,  after  selling  from  a  cask  of  wine 
15  gallons  more  than  -J  of  the  whole,  found  that  the 
number  of  gallons  left  was  just  3  times  the  number 
of  gallons  sold ;  how  many  gallons  did  the  cask  con- 
tain at  first  ? 

20.  If  a  store  be  worth  81000,  and  |  of  the  value 
of  the  store  be  equal  to  -|  of  2^^-  times  the  value  of  the 
goods  it  contains,  what  is  the  value  of  the  goods  ? 

21.  Two  boys,  comparing  their  money,  one  said 
he  had  50  cents  ;  the  other  said,  "  ^^  of  your  money 
is  just  ^^^  of  6  times  my  money ; "  how  many  cents 
had  the  latter  boy  ? 

22.  The  distance  from  Boston  to  Albany  is  200 
miles,  and  f  of  this  distance  is  f  times  i  the  distance 
from  Albany  to  Niagara  Falls,  lacking  5  miles ;  what 
is  the  distance  from^Boston  to  Niagara  Falls  ? 

23.  The  distance  from  Chicago  to  Alton  is  268 
miles,  and  f  of  this  distance  plus  15  miles,  is  4^  times 
f  of  the  distance  from  Alton  to  St.  Louis  ;  what  is 
the  distance  from  Chicago  to  St.  Louis  ? 

24.  40  is  I  of  I  of  -^-"of  8  times  what  number  ? 


110  •      INTELLECTUAL   ARITHMETIC. 

71.     1.    4  of  35  is  |-  of  how  many  thirds  of  18  ?  * 

Analysis.  Of  as  many  thirds  of  IQ  as  \  of  \%  is 
contained  times  in  9  ti^nes  \  of  4  times  4  of  35  ;  \  of 
35  is  5,  and  4  times  5  is  20 ;  \  of  20  is  4,  and  9  times  4 
is  36  ;  -J  o/  18  is  0,  a?ic?  6  is  contained  in  36,  6  times. 
Therefore,  4  o/  35  is  %of  ^  thirds  of  18. 

2.  f  of   42  is   4-  of  how  many  fifths  of  35  ? 

3.  I  of    96  is   I  of  how  many  eighths  of  24  ? 

4.  I  of  180  is  |~  of  how  many  tenths  of  50  ? 

5.  I   of    84  is  I   of  how  many  sixths  of  48  ? 

6.  2V  ^f  1^^  is  -^  of  how  many  ninths  of  45  ? 

7.  I"  of    45  is  -^^  of  how  many  halves  of  48  ? 

8.  -j\  of    77  is  I  of  how  many  twelfths  of  72  ? 
^9.  -1-1-  of    30  is  f   of  how  many  thirds  of  21  ? 

10.  -^^  of    28  is  2%  of  how  many  fourths  of  24  ? 

11.  f  of    18  is  ^\  of  how  many  twelfths  of  GO  ? 

12.  I  of    80  is  -|  of  how  many  fourths  of  40  ? 

13.  |-  of    42  is  -f^  of  how  many^  eighths  of  72  ? 

14.  y%  of    39  is  2%-  of  how  many  ninths  of  180  ? 

15.  I  of  |-  of  18  is  4  times  what  part  of  35  ? 

Ai^ALYSis.  Buch  a  iKirt  of  35,  as  35  is  contained 
times  in  \  of  5  times  ^  of  6  titnes  \  of  IS\  4  o/*  18  is 
6,  and  6  tiines  6,  is  36  ;  ^  of  36  is  4,  and  5  ^wzes  4  ?^ 
20  ;  I  o/"  20  is  5,  a;?  J  35  «s  contained  in  6,  /^  or  4 
times.    TJierefore  f  0/  |  0/  18  is  4  ^Jfwe^  4»  or  4,  0/  35. 

16.  i  of  I  of   40  is  3  times  what  part  of  24  ? 

17.  -|  of  -3-  of    49  is  2  times  what  part  of  28  ? 

18.  I  of  ^^  of  100  is  9  times  v/hat  part  of  25  ? 

19.  I  of  I  of    48  is  7  times  what  part  of  35  ? 

20.  -5-^  of  -|  of    GO  is  7  times  what  part  of  64  ? 

21.  f  of  I  of    80  is  3  times  what  part  of  98  ? 

*  Observe  the  "  changes  "  in  the  Appendix,  71,  page  171. 


73.]  INTELLECTUAL   ARITHMETIC.  Ill 

7*2,     1.    I  of  36  is  4  of  how  many  times  f  of  42  ?- 

ANALYSTS.  Of  as  many  times  §  of  42  05  2  ^/mes  ^ 
of  42  /5  contained  times  in  9  ?/??ze5  |  q/"  4  times  \  of 
36  ;  4  of  36  ?.«  12,  w?<:7  4  ^wz^'s  12  is  48  ;  j  o/  48  is  12, 
«;?c^9  ^/me5  12  is  108  ;  ^  o/"  42  ?5  6,  and  2  f/«?e5  C  is 
12,  <7??f?  12  /5  contained  in  108,  9  ^/mes.  Therefore  | 
0/  36  es  I  0/  9  ^zV?2e5  f  o/  42. 

2.  |-  of  64  is  I   of  how  many  times  |  of  15  ? 

3.  |-  of  27  is  I  of  how  many  times  |  of  bQ  ? 

4.  -J  of  81  is  |-  of  how  many  times  I  of  28  ? 

5.  |-  of  50  is  \^-  of  how  many  times  |  of  60  ? 

6.  -|  of  36  is  -^j  of  how  many  times  ^  of  27? 

7.  f  of  32  is  2^  of  how  many  times  -|  of  45  ? 

8.  -j^Q-  of  150  is  I  of  how  many  times  |  of  40  ? 

9.  "I   of  108  is  -^Q  of  how  many  times  |  of  16|-t 

10.  ^^3-  of    6d  is  -^  of  how  many  times  |  of  |  of  50  ? 

11.  f  of    60  is  I  of  how  many  times  |  of  25  ? 

12.  I  of    72  is  I  of  how  many  times  J-  of  -4-  of  70  ? 

13.  "I  of  i  of  84  is  |-  of  how  many  times  ^  of  |- 
of  96  ?  '^  \, 

14.  |-  of  "I  of  90  is  4  of  f  of  how  many  times  -| 
of  I  of  20  ? 

15.  |-  of  |-  of  36  is  |-  of  I  of  how  many  times  | 
of  f  of  120  ? 

16.  A  man  pays  8400  rent,  and  -|  of  this  is  jnst  | 
of  i-  of  twice  his  annual  income ;  what  is  his  annual 
incc  me  ? 

17.  A  boy  being  asked  his  nge  said  tliat  18  years  was 
2  years  less  than  |  times  |  of  his  age  ;  how  old  was  he  ? 

18.  The  distance  from  Baltimore  to  Washington 
is  39  miles ;    if  5  miles  be  subtracted  from  |  of   this 

*  For  "  changes"  see  Appendix,  73,  Page  173. 


Hi  INTELLECTUAL   ARITHMETIC.  [73. 

distance,  the  remainder  will  be  |  times  |  the  distance 
from  Philadelphia  to  Baltimore  ;  what  is  the  distance 
from  Philadelphia  to  Washington  ? 

19.  Mr.  B.,  who  is  64  years  of  age,  is  2|  times  as 
old  as  his  eldest  son,  and  his  eldest  son  is  2|  times 
as  old  as  his  youngest  brother  ;  what  is  the  difference 
in  the  ages  of  the  two  brothers  ? 

20.  Oscar  earned  a  certain  number  of  pennies ; 
Rufus  earned  |^as  many  minus  4,  and  David  earned 
I  as  many  as  Kufus,  plus  7  ;  Oscar  earned  50  pen- 
nies ;  how  many  did  Rufus  and  David  earn  ? 

21.  A  man  put  his  money  into  4  packages  ;  in  the 
first  he  put  |,  in  the  second  i,  in  the  third  -J,  and  in 
the  fourth  |24  ;  how  much  money  had  he  ? 

22.  A  sold  I  of  his  sheep  on  Monday ;  Tuesday 
he  bought  |  as  many  as  he  had  sold ;  he  then  had  60 
sheep  ;  how  many  had  he  at  first  ? 

23.  Mrs.  D.'s  shawl  cost  |30  ;  |  of  the  cost  of  the 
shawl  was  -|  of  6  times  the  cost  of  her  dress ;  what 
was  the  cost  of  her  dress  ? 

24.  B  and  C  engaging  in  play,  B  had  f  as  much 
money  as  C  ;  C  gained  ^16,  which  was  |  of  1|^  times 
as  much  as  he  commenced  with  ;  how  much  did  he 
commence  with,  and  how  much  had  B  left  ? 

25.  A  farmer,  being  asked  how  many  sheep  he 
had,  replied  that  he  had  just  sold  150,  and  that  |  the 
number  he  had  sold  was  6  times  |  of  what  he  had 
left ;  how  many  had  he  left  ? 

26.  Mr.  S.  gave  |  of  1}  times  his  ready  money  for 
a  buggy,  I  of  what  was  left  for  a  harness,  and  had 
$12  remaining ;  what  did  he  pay  for  the  buggy  ? 

27.  A  paid  i^4800  for  his  farm ;  f  of  this  is  4|- 
times  I  of  2  times  what  it  cost  to  build  the  house ; 
what  was  the  cost  of  the  house  ? 

28.  1  of  f  of  80  is  I  of  I  of  how  many  times  | 
of  I  of ''lOO  ? 


73.]  INTELLECTUAL   ARITHMETIC.  113 

CHAPTER  YII. 
KATIO    AND    PKOPORTION. 

73.     1.   What  part  of  4  is  1  ?  of  4  is  3  ?  * 

Analysis.  Si7ice  1  is  ^  o/  4,  3  mttst  be  3  times  ^  paH 
of  4,  or  f  of  4.      Therefore  3  is  f  of  4. 

2.  What  part  of    3  is    1  ?  of    3  is    2  ? 

3.  What  part  of    7  is    1  ?  of    5  is    3  ? 

4.  What  part  of    8  is    2  ?  of    9  is    5  ? 

5.  What  part  of  10  is    7  ?  of  13  is    9  ? 

6.  What  part  of    8  is    9  ?  of  12  is    7  ? 

7.  What  part  of  16  is  11  ?  of  20  is  17  ? 

8.  What  part  of  40  is    9  ?     What  is  the  ratio  ? 

9.  What  part  of  30  is  27  ?     What  is  the  ratio  ? 

10.  What  part  of     |  is    f  ?     What  is  the  ratio  ? 

Analysis.  |  :=  |f,  and  §  =  |n. ;  the  ratio  of  |f  to 
^1  is  the  same  as  that  of  their  numerators^  10  to  12  :  what 
imrt  of  12  is  10  'i  \%^  %-  Therefore  \  is  |  o/f,  and  the 
ratio  is  f . 

11.  What  part  of    |  is  }  ?  of  f  is  J  ? 

12.  What  part  of    |  is  |  ?  of  j\  is  1  ? 

13.  What  part  of   f  is  f  ?  of  ^\  is  |  ? 

14.  What  part  of  5^  is  |  ?  of  |-  is  f  ? 

15.  What  part  of  -j\  is  |  ?     What  is  the  ratio  ? 

16.  What  part  of  5    is  f  ?     What  is  the  ratio  ? 

17.  AVhat  part  of  7    is  f  ?  of  3^  is  2  ? 

18.  What  part  of  4|  is  f  ?  of  7^  is  3^  ? 

19.  What  part  of    |  is  2  ?  of  2|-  is  If  ? 

20.  What  part  of  3^  is  5  ?  of    f  is  6  ? 

*  The  quotient  arising;  from  dividing  one  nnmber  by  another  is  called 
the  ratio.  Thus,  what  part  of  4  is  1  ?  It  is  1  divided  by  4,  equal  to  |,  the 
reiiio.    What  part  of  4  is  3  ?    It  is  3  divided  by  4,  equal  to  |,  the  ratio, 

8 


114  INTELLECTUAL   AEITHMETIC.  [74, 

74.     1.   What  part  of  25  dollars  is  5  dollars  ?  is 
10  dollars  ? 

2.  What  part  of  16  pounds  is  4  pounds  ?   is  7 
pounds  ?  is  12  pounds  ? 

3.  What  part  of  1  bushel  is  1  peck  ?  is  2  pecks 
and  4  quarts  ?  is  6  quarts  ? 

4.  What  part  of  1  pound  is  12  shillings  ? 

6.  What  part  of  1  dollar  is  20  cents  ?  is  5  dimes  ? 

6.  What  part  of  1  cwt.  are  15  pounds  ? 

7.  What  part  of  1  cwt.  are  6  lbs.  ?  9  lbs.  ? 

8.  What  part  of  1  ton  is  14  cwt.  ?  15  cwt.  ?  18  cwt.  ? 

9.  What  part  of  3  pounds  is  10  oz.  ?  is  1  lb.  6  oz.  ? 

10.  What  part  of  1  foot  is  3  in.  ?  10  in.  ?  11  in.  ? 

11.  What  part  of  2  yds.  is  1  foot  ?  1  foot  10  inches  ? 

12.  What  part  of  1  mile  is  3  furlongs  ?  5  furlongs 
20  rods  ? 

13.  What  part  of  1  mile  is  140  rods  ?  160  rods  ? 

14.  What  part  of  1  gallon  is  1  quart  ?  1  pint  ? 

15.  What  part  of  1  hhd.  is  5  gallons  ?  21  gallons  ? 

16.  What  part  of  1  quart  is  1  pint  ?  2  gills  ? 

17.  What  part  of  1  liovir  is  15  minutes  ?  40  min- 
utes ? 

18.  What  part  of  1  day  is  b  nours  ?  8  hours  ?  16 
hours  ? 

19.  What  part  of  3  weeks  is  2  days  ?  5  days  ?  9 
days  ? 

20.  What  part   of  1  year  is  3  weeks  ?  7  weeks  ? 

21.  What  part  of  5  pounds  6  ounces  is  3  pounds 
10  ounces  ? 

22.  What  part  of  3  lihd.  is  1  hhd.  22  gallons  ? 

23.  What  part  of  1  mile  3  fur.  is  4  fur.  20  rods  ? 

24.  What  part  of  3  pecks  is  6  quarts  1  pint  ? 

25.  Two  pounds  is  what    part   of  1  cwt.  ?  of  2 
cwt.  ? 

26.  Eight  inches  is  what  part  of  a  foot  ?  of  2  feet  ? 
of  1  yard  ?  of  4  yards  ? 


74.]  INTELLECTUAL   ARITHMETIC.  115 

27.  Three  quarts  is  what  part  of  a  gallon  ?  of  5 
gallons  ?  of  10  gallons  ?  of  1  hhd.  ? 

28.  What  part  of  9  miles  is  |  of  8  miles  ? 

29.  What  part  of  4|  acres  is  |  of  3-|  acres  ? 

80.  A  man,  having'llS,  gave  |3|  lor  a  hat,  and 
84J  for  a  pair  of  boots  ;  what  part  of  his  money  did 
he  use,  and  what  part  had  he  left  ? 

31.  A  farmer,  having  160  bushels  of  wheat,  sold 
|-  of  I  of  it,  floured  |  of  |  of  it,  and  kept  the  re- 
mainder for  seed  ;  what  part  of  the  whole  did  he  use 
for  each  purpose  ? 

32.  If  I  have  sold  |  of  i  of  120  sheep,  what  part 
of  the  whole  flock  have  I  left  ? 

33.  One  man  can  walk  4|  miles  while  another 
walks  3|  miles  ;  what  part  of  the  distance  that  the 
first  walks  does  the  second  walk  ? 

34.  A  gentleman  paid  |-  of  |39|  for  a  coat,  and 
89|-  for  a  pair  of  pantaloons  ;  how  many  times  as 
much  did  he  pay  for  the  coat  as  for  the  pantaloons  ? 

35.  Paid  $T|-  for  a  barrel  of  flour,  and  1|  times 
as  much  for  a  ton  of  hay ;  what  was  the  cost  of  the 
hay? 

36.  A  man  bought  a  horse  for  1225,  and  a  car- 
riage for  ^  of  I  of  this  sum  ;  what  part  of  |125  did 
the  carriage  cost  ? 

37.  If  a  vessel  sail  40  miles  in  5  hours,  what  part 
of  144  miles  will  she  sail  in  9  hours  ?  how  many 
miles  ? 

38.  A  man  gave  to  his  3  sons  360  acres  of  western 
land  ;  to  the  first  he  gave  |  of  it,  to  the  second  |-  of 
3|-  times  as  much,  and  the  remainder  he  gave  to  the 
third  ;  what  part  of  the  whole  did  each  receive  ?  how 
many  acres  ? 

39.  A  merchant  gained  on  a  hogshead  of  sugar 
|-  of  $46|,  which  was  |-  of  2  times  what  it  cost  him  ; 
what  did  it  cost  him  ?  what  part  of  the  cost  was  the 
gain  ? 


116  INTELLECTUAL   ARITHMETIC.  [_75. 

7&.  1.  If  6  cords  of  wood  cost  |15,  what  will 
4  cords  cost  ? 

Analysis.  Four  cords  are  f,  or  %  of  ^  cords.  If 
G  cords  of  wood  cost  $15,  4  cords  will  cost  f  of  $15  ; 
\  of  $15  {5  $5,  and  |  of  $15  is  2  times  $5,  or  $10. 
Therefore^  S;c. 

Or,  Me  ;;«*/>//  may  wse  the  form  of  analysis  used  in  section 
2^5  onjnige  41. 

2.  If  9  pounds  of  sugar  cost  75  cents,  what  will 
12  pounds  cost  ? 

8.  If  G  men  can  cut  45  cords  of  wood  in  3  days, 
how  many  cords  can  8  men  cut  in  the  same  time  V 

4.  If  31  yards  of  cloth  cost  $10i ,  how  much  will 
7  yards  cost  ? 

5.  If  4|  pounds  of  butter  cost  QQ  cents,  what  will 
2 1  pounds  cost  ? 

6.  If  a  mechanic  earn  13|-  shillings  in  1^-  days, 
how  much  can  he  earn  in  a  week  ? 

7.  If  %1\  will  buy  3|-  cords  of  wood,  how  many 
cords  can  be  bouglit  for  $10 J-  ? 

8.  If  -J  barrel  of  flour  cost  ^^,  what  will  |  of  a 
barrel  cost  ? 

Analysis.  What  part  of  ^  is  ^"^  i  =  ^,  and  §  =  |- ; 
the  ratio  of  ^  to  ^  is  the  same  as  of  3  ^o  4,  =  |-.  Then^  since 
4  barrel  of  four  cost  $4^,  §  0/  a  barrel  will  cost  ^  of  $4^ ; 
lof  ^  =z  %6-  —  $6.      Therefore,  ^-c. 

9.  If  a  man  can  run  6  miles  in  f  of  an  hour,  how 
far  can  he  run  in  3^  hours  ? 

10.  How  many  yards  of  carpeting  |-  of  a  yard 
wide  are  equal  to  12  yards  -|  of  a  yard  wide  ? 

11.  If  a  staff  3  feet  long  cast  a  shadow  5  feet  in 
length,  what  would  be  the  length  of  the  shadow  cast 
by  a  pole  13  feet  long  ? 

12.  If  the  sawing  of  |-  of  a  cord  of  wood  cost  6^ 
shillings,  what  would  the  sawing  of  3|-  cords  cost  ?  " 


75.]  INTELLECTUAL   ARITHMETIC.  117 

13.  John  earns  9  cents  as  often  as  James  earns  15 
cents ;  when  John  has  earned  63  cents,  how  much 
has  James  earned  ? 

11.  Two  persons  start  from  different  points  and 
travel  towards  each  otlier ;  the  lirst  one  travels  T 
miles  while  the  otlier  travels  5  miles,  and  when  they 
meet  the  first  one  has  traveled  70  miles ;  how  far 
apart  were  they  when  they  started  ? 

15.  If  4  men  can  build  a  wall  60  feet  Ions:  in  6 
dsijs,  in  what  time  can  3  men  build  a  wall  yO  feet  in 
length  ? 

Analysis.  In  J  of  ^  of  Q  days,  ickich  are  12  days. 
Or  thus  :  if  it  ivill  take  4  men  6  days  to  build  a  wall  60  feet 
long,  it  will  take  1  man  4  times  6  days,  or  24  days,  and  3 
men  can  do  it  in  ^  of  24,  or  8  days  ;  to  build  a  icall  1  foot 
long  ivill  require  ^'^  of  8,  or  -^^  days,  and  to  build  a  ivall 
'dO  feet  long  ivill  require  90  times  as  many  days,  or  DO  times 
-^fj,  equal  to  12  days.      Tlierefore,  S^c. 

16.  If  5  men  can  do  a  piece  of  work  in  10  days, 
how  many  men  will  do  a  piece  of  work  4  times  as 
larore  in  20  davs  ? 

17.  If  a  man  perform  a  journey  in  8  days,  by 
traveling  9  hours  a  day,  how  many  days  will  he  re- 
quire to  perform  the  same  journey,  if  he  travel  12 
hours  a  day  ? 

18.  If  5  horses  eat  11  tons  of  hav  in  1  month,  how 
many  tons  will  6  horses  eat  in  2|-  months  ? 

19.  How  many  days  will  it  take  5  men  to  earn 
$11| ,  if  3  men  earn  8J  in  ^  of  a  day  ? 

20.  If  1  horse  eat  1^  bushels  of  oats  in  3  davs,  in 
how  many  days  will  4  horses  eat  49  bushels  ? 

21.  If  a  barrel  of  flour  will  supply  a  family  of  4 
persons  5  weeks,  how  much  will  supply  a  family  of 
3  persons  2^  weeks  ? 

22.  If  3  furnaces  consume  124  tons  of  coal  in  7 
days,  how  long  will  VJ^  tons  last  5  furnaces  ? 


118 


INTELLECTUAL  ARITHMETIC. 


[76. 


76. 


CHAPTER  YIII. 
PERCENTAOE. 


The  terms^ percentage  and  per  cejit.,s\gmfy  hy  the  hun- 
dred^ or  hundredths,  that  is,  a  certain  number  of  parts  of  each 
one  hundred  parts,  of  whatever  denomination.  Thus,  by  5 
per  cent,  is  meant  o  cents  of  every  100  cents,  $5  of  every 
$100,  5  bushels  of  every  100  bushels,  &c.  Therefore,  5 
per  cent,  equals  5  hundredths,  (y^^,)  or  ^V-  ^  P^i"  cent.,  8 
hundredths,  (-fnuO  o^'  i^h  ^^  ^^^^  given  number  or  quantity. 

1.  A  man,  having  $40,  lost  3  per  cent,  of  it ;  lioW 
many  dollars  did  he  lose  ? 

Analysts.  Si.jice  he  lost  3  per  cent,,  or  yf^,  on  $1, 
on  $40  he  lost  40  times  y^^,  or  \l%  of  $1,  equal  to  $1^. 
Therefore,  S^^c. 

s    5  per  cent,  of  |25  ?  of  ISO  ?  of   $45  ? 
s    7  per  cent,  of  |15  ?  of  140  ?  of  $200  ? 
s    6  per  cent,  of  $18  ?  of  $37  ?  of   $54  ? 
s    3  per  cent,  of    50  bushels  of  corn  ? 
s  10  per  cent,  of  160  tons  of  plaster  ? 
s  25  per  cent,  of    96  gallons  of  wine  ? 
s  12  per  cent,  of  331  pounds  of  sugar  ? 
s  15  per  cent,  of  110  barrels  of  flour  ? 
s    8  per  ceht.  of    28  yards  of  cloth  ? 
s    f  per  cent,  of  $45  ? 


2.  What 

3.  What 

4.  What 
6.  What 

6.  What 

7.  What 

8.  What 
0.  What 

10.  What 

11.  What 


Analysts.     Si7ice  1  per  cent  of  $45  is  yV^,  %  of  I  per 
cent,  is  f  of  j%%  or  -fjj^,  equal  to  $f^.      77ierefore,  Sfc. 


12.  What 

13.  What 

14.  What 

15.  What 

16.  What 


s    I  per  cent,  of  $28  ?  of  $44  ?  of  $36  ? 
s    i  per  cent,  of  $63  ?  of  $120  ? 
s    I  per  cent,  of  30  barrels  of  cider  ? 
s  3|-  per  cent  of  70  sheep  ?  of  35  cows  ? 
s  2|  per  cent,  of  34  hundred  weight  ? 


77.]  INTELLECTUAL   ARITHMETIC.  119 

17.  A  man  bought  75  barrels  of  apples,  and  on 
opening  tliem,  found  8  per  cent,  of  them  spoiled ; 
how  many  barrels  did  he  lose  ? 

18.  If  I  have  1200  deposited  in  the  bank,  and 
draw  out  15  per  cent,  of  it,  how  much  remains  ? 

19.  A  farmer,  having  176  sheep,  sold  75  per  cent, 
of  them,  and  kept  the  remainder ;  how  many  did  he 

keep? 

20.  A  young  man,  having  |104,  lost  12^  per  cent, 
of  it  in  gambling;  how  many  dollars  did  he  lose, 
and  what  per  cent,  of  the  whole  had  he  left  ? 


77.  1.  What  fraction  of  a  number  is  8  per  cent, 
of  it  ? 

Analysis.  Since  1  per  cent,  is  y^^,  8  per  cent,  is  8 
times  y^g-,  or  yf  ^,  =  ^%.  Therefore  8  per  cent,  equals  /^ 
of  any  number  or  thing. 

2.  What  fraction  of  a  number  is  6  per  cent.  ?  7 
per  cent.  ?  10  per  cent.  ?  12^  per  cent.  ? 

3.  What  fraction  of  a  number  is  Q\  per  cent.  ? 
16f  per  cent.  ?  20  per  cent.  ?  37|-  per  cent.  ?  40  per 
cent.  ? 

4.  If  you  have  $120,  and  lose  SSJ  per  cent,  of  it, 
what  part  of  it  will  you  lose  ? 

5.  James,  having  250  marbles,  lost  40  per  cent,  of 
them  at  play ;  what  part  of  the  whole  had  he  left, 
and  how  many  did  he  lose  ? 

6.  What  per  cent,  of  a  barrel  of  flour  is  |^  of  it  ? 

Analysis.  Since  the  whole  of  any  number  or  thing  is 
equal  to  100  per  cent.,  f  of  one  barrel  of  flour  is  equal  to 
f  (t/*  100  per  cent.,  or  40  per  cent.      Therefore,  S^c. 

7.  If  a  man  save  f  of  his  income,  what  per  cent, 
does  he  spend  ? 

8.  If  a  merchant  invest  f  of  his  money  in  dry 
goods,  what  per  cent,  does  he  invest  ? 


120  INTELLECTUAL   ARITHMETIC.  [78. 

78.  1.  A  farmer,  having  20  sheep,  lost  5  of  them 
by  disease  ;  what  per  cent,  did  he  lose  ? 

Analysis.  Since  20  sheep  are  100  per  cent.,  or  all  that 
he  had,  5  sheep  are  -^q-,  or  ^,  of  all  he  had;  and  ^  of  100 
per  cent,  is  25  per  cent.      Therefore,  ^c. 

2.  What  per  cent,  of  21  is  7  ? 

3.  What  per  cent,  of  50  is  5  ?  10  ?  20  ?  25  ? 

4.  What  per  cent,  of  140  is  $5  ?  $8  ?  $25  ?  130  ? 

5.  What  per  cent,  of  18  pounds  is  3  pounds  ?  12 
pounds  ? 

6.  What  per  cent,  of  42  miles  is  6  miles  ?  7  miles  ? 

7.  What  per  cent,  of  12i-  is  2}  ?  Q>\  ? 

8.  What  per  cent,  of  30''is  12"?  15  ?  20  ? 

9.  What  per  cent,  of  18  is  9  ?  12  ?  15  ? 

10.  11  is  what  per  cent,  of  9  ?  of  15  ?  of  21  ? 

11.  2|  is  what  per  cent,  of  7^-  ?  of  12^-  ?  of  10  ? 

12.  l^is  what  per  cent,  of  3l"?  of  16|"?  of  20  ? 

13.  -1/  is  what  per  cent,  of  8  ?  of  12  ?  of  20  ? 

14.  If  from  a  hogshead  of  molasses  a  grocer  draw 
42  gallons,  what  per  cent,  of  the  whole  will  remain  ? 

15.  From  a  box  of  tea  containing  60  pounds,  15 
pounds  were  sold  at  one  time,  and  25  pounds  at 
another ;  what  per  cent,  of  the  whole  remained  un- 
sold ? 

16.  In  a  heap  of  potatoes  containing  150  bushels, 
3  bushels  of  every  5  are  bad  ;  what  per  cent,  are 
bad,  and  how  many  bushels  are  good  ? 

17.  A  gambler,  liaving  |250,  lost  $80  at  play ; 
what  per  cent,  of  his  money  did  he  lose,  and  what 
per  cent,  had  he  left  ? 

18.  James,  having  62^-  cents,  gave  37|^  for  a  book  ; 
what  per  cent,  of  his  money  had  lie  left  ? 

19.  A  grocer,  having  a  barrel  of  sugar  containing 
200  pounds,  sold  \  of  it  at  one  time,  and  ^  of  tlie 
remainder  at  another  time ;  what  per  cent,  remained 
unsold  ? 


79.]  INTELLECTUAL   ARITHMETIC.  121 

79.  1.  A  person  collects  ^240,  and  receives  5 
per  cent,  commission  on  what  he  collects  ;  what  com- 
pensation does  he  receive  ? 

Analysis.  Since  the  cojnmission  is  5  per  cent.,  or  y§^, 
equal  to  ^-V?  ^f  ^^^^  *^^"^  collected,  he  receives  ^'g-  of  $240, 
which  is  $12.      Therefore,  Sfc. 

2.  What  will  be  the  expense  of  collecting  a  note 
of  8800,  at  10  per  cent,  commission  ? 

3.  What  mnst  be  paid  for  collecting  a  tax  of  $300, 
allowing  12|  per  cent,  commission  ? 

4.  An  agent  sells  81200  worth  of  merchandise,  at 
25  per  cent,  commission ;  how  much  will  he  receive 
for  his  services  ? 

5.  An  auctioneer  sold  goods  to  the  amount  of 
$500 ;  what  will  his  commission  amount  to,  at  2^ 
per  cent.  ? 

6.  Paid  an  attorney  8^  per  cent,  to  collect  a  debt 
of  $640  ;  how  much  did  he  receive  for  his  services  ? 

7.  If  a  man  fail  in  business,  and  can  pay  but  40 
per  cent,  of  his  debts,  how  much  will  a  creditor 
receive  on  a  debt  of  8175  ? 

8.  Bought  81000  worth  of  books,  receiving  a  com- 
mission of  3|  per  cent. ;  how  much  did  I  receive  for 
my  services  ? 

9.  If  a  broker  sell  8600  worth  of  New  York  Cen- 
tral Railroad  stock,  and  charge  f  per  cent,  for  sell- 
ing, how  much  will  he  receive  ? 

10.  At  4.  of  1  per  cent.,  what  will  be  the  expense 
of  negotiating  a  bill  of  exchange  of  8625  ? 

11.  A  broker  in  Chicago  exchanged  81200  on  the 
Chemical  Bank  of  New  York,  at  |  per  cent. ;  what 
amount  of  brokerage  did  he  receive  ? 

12.  A  real  estate  agent  sells  a  house  and  lot  for 
82000,  and  charges  1^  per  cent,  commission  for  sell- 
ing ;  how  much  does  he  receive  ? 


122  INTELLECTUAL   ARITHMETIC.  [80, 

8I>.  1.  A  merchant  sends  his  agent  1780  to  ex- 
pend for  merchandise,  after  deducting  his  commis- 
sion of  4  per  cent. ;  what  sum  will  he  expend  ? 

Analysis.  The  money  to  he  exjjended  is  \%^  of  itself 
and  the  commission  y^ij,  or  ^y,  of  this  sum;  hence  the 
whole  amount  se7it  to  the  agent  is  |^^-,  or  §|.  Since  $780 
is  5.|,  _i_.  is  2^g.  of  $780,  or  $30,  his  commission  ;  and  f-|  is 
25  times  30,  or  $750,  the  sum  to  be  expended. 

2.  I  gave  a  broker  $810  to  invest  in  bank  stock, 
after  deducting  his  commission  of  1^  per  cent.  ;  what 
was  his  commission,  and  how  much  did  he  invest  ? 

3.  A  distiller  sent  Mr.  B.  81550,  with  which  to  buy 
corn,  after  deducting  his  commission  of  3^  per  cent. ; 
how  much  did  he  expend,  and  how  much  did  his 
commission  amount  to  ? 

4.  How  many  bushels  of  wheat,  at  $1  a  bushel, 
can  an  agent  buy  for  $1230,  and  retain  2 J-  per  cent, 
commission  for  his  trouble  ? 

5.  A  farmer  employed  a  man  to  thresh  his  wheat, 
agreeing  to  give  him  12  per  cent,  of  all  he  threshed ; 
how  many  bushels  must  he  thresh  that  the  farmer 
may  retain  QQ  bushels? 

Analysis.  Since  the  thresher  received  -^^^,  or  -^-^  of  all 
he  threshed^  the  farmer  received  the  difference  between  \%%^ 
or  §^  and  ^\,  which  is  |f.  The?!  66  bushels  is  §^  of  the 
whole  number  of  bushels  threshed;  since  66  bushels  is  ^f, 
^\  ^5  ^V  of  66,  or  3  bushels,  and  f  |  is  25  times  3  bushels, 
or  75  bushels.      Therefore,  Sfc. 

6.  What  amount  must  be  collected  on  a  rate  bill, 
that  the  collector  may  retain  his  fee  of  5  per  cent., 
and  pay  over  $228  ? 

7.  What  amount  of  accounts  must  an  individual 
collect  in  order  to  pay  over  $1100,  and  retain  8J  per 
cent,  for  collecting  ? 


§3, J  INTELLECTUAL   ARITHMETIC.  123 

§1.  1.  'Wh^t  must  be  paid  for  insuring  a  house 
and  furniture  for  $1000,  at  1^  per  cent,  premium  ?  * 

Analysis.  Since  the  premium  is  1^  per  cent.,  or  ^-S^, 
equal  to  ^V  ^f  ^^^^  ccmount  insured,  the  prejnium  on  $1000 
will  he  -gi^  of  $1000,  or  $12^.      Therefore,  &>c. 

2.  What  will  be  the  premium  for  insuring  200 
barrels  of  flour,  valued  at  $1200,  at  4  per  cent.  ? 

3.  What  must  I  pay  annually  for  an  insurance  of 
$900  upon  my  life,  at  2'J  per  cent.  ? 

4.  What  must  be  paid  for  insuring  a  case  of  cloths, 
valued  at  $600,  at  If  per  cent,  premium  ? 

5.  What  is  the  annual  premium  of  insurance,  at 
I  per  cent.,  on  a  building  valued  at  $4000  ? 

6.  If  a  merchant  has  his  stock  of  goods  insured 
for  $2500,  at  |  of  1  per  cent.,  what  is  the  premium  ? 

7.  A  man  owns  f  of  a  boat  load  of  grain,  valued 
at  $1600,  and  insures  his  interest  at  If  per  cent ; 
what  premium  does  he  pay  ? 

8.  At  2  per  cent.,  what  amount  of  insurance  can 
I  obtain  for  $18  premium  ? 

Analysis.  Si7ice  2  per  cent,  premium  is  y§^,  or  -^-^  of 
the  amount  insured,  $18,  the  given  premium,  will  he  equal 
to  -1^  of  the  required  amount  of  insurance  ;  $18  is  ^^  of  50 
times  $18,  equal  to  $900.      TJierefore,  Sfc. 

9."  At  3  per  cent.,  what  amount  of  insurance  can 
be  obtained  on  a  house  for  $75  ? 

10.  At  ^  per  cent.,  what  amount  of  insurance  can 
be  obtained  on  a  boat  load  of  flour,  for  $24  ? 

11.  What  amount  of  insurance  can  be  had  for 
$45,  upon  a  car  load  of  horses,  at  4~|^  per  cent.  ? 

12.  If  the  rate  is  If  per  cent.,  and  the  premium 
paid  is  $91,  what  will  be  the  amount  of  insurance 
obtained  on  a  store  and  its  contents  ? 

*  The  sum  paid  for  insurance  is  called  the  premium. 


124  INTELLECTUAL  ARITHMETIC.  [82. 

8S.  1.  If  a  man  buy  a  horse  for  |90,  for  how 
much  must  he  sell  him  to  gain  20  per  cent.  ? 

Analysis.  Since  he  c/ains  20  per  cent.,  or  y^.o^,  equal  to 
^  of  what  the  horse  cost  hi)7i,  he  must  sell  him  for  f  o}'  what 
he  cost;  -i  of  $90  is  $18,  and  |  of  $90  is  6  times  $18,  or 
$108.      Therefore,  S)'C. 

2.  A  sleigh  was  bought  for  |50,  and  sold  for  8  per 
cent,  more  than  it  cost ;  what  was  it  sold  for  ? 

3.  Bought  a  quantity  of  sugar  for  $84,  and  sold  it 
at  an  advance  of  12|^  per  cent ;  what  was  it  sold  for  ? 

4.  A  grocer  bought  some  tea  for  $45,  but  finding 
it  damaged,  he  was  obliged  to  sell  it  at  a  loss  of  10 
per  cent.  ;  what  did  he  sell  it  for  ? 

5.  Paid  $12  for  15  yards  of  cloth ;  what  must  it 
be  sold  for  a  yard  to  gain  25  per  cent.  ? 

6.  A  drover  bought  60  sheep  for  $180,  and  sold 
them  at  a  loss  of  20  per  cent,  on  the  cost ;  what 
did  he  receive  per  head  for  them  ? 

7.  A  grocer  bought  440  lemons  for  $12,  and  after 
throwing  away  10  per  cent,  of  them,  lacking  4,  as 
worthless,  he  sold  the  remainder  so  as  to  gain  88|- 
per  cent,  on  the  cost  of  the  whole ;  what  did  he  sell 
them  for  apiece  ? 

8.  Bought  6  barrels  of  flour  for  $40 ;  for  what 
must  it  be  sold  a  barrel  to  gain  5  per  cent,  on  the 
cost  ? 

'9.    If  I  buy  eggs  at  10  cents  a  dozen,  how  must 
I  sell  them  to  gain  30  per  cent.  ? 

10.  A  speculator  bought  a  quantity  of  pork  for 
$500,  and  sold  it  at  a  loss  of  7  per  cent. ;  with  the 
proceeds  he  bought  another  quantity,  upon  which  lie 
gained  20  per  cent.  ;  what  wa  his  gain  on  the  whole  ? 

11.  Bought  hay  at  $14  dollars  a  ton,  which  was 
12|  per  cent,  less  than  the  market  price  ;  what  was 
the  market  price  ? 


83.]  INTELLECTUAL   ARITHMETIC.  125 

83.  1.  What  is  gained  per  cent,  by  selling  clover 
seed  for  |6,  that  cost  |4  ? 

Analysis.  The  whole  gain  is  equal  to  the  difference 
between  $6  and  $4,  which  is  $2.  Since  $4  gain  S$2,  or  -^ 
of  Itself,  equal  to  Y^gV?  ^^^^  ^«ui  will  be  50  per  cent.  There- 
fore, ^c. 

2.  What  per  cent,  is  gained  by  selling  pork  for 
$7  a  hundred  weight,  that  cost  |6  ? 

3.  What  will  be  gained  by  expending  $500  for 
sugar,  when  it  can  be  bought  for  8  cents,  and  sold 
for  8|-  cents  a  pound  ? 

4.  "if  I  buy  1300  worth  of  sheep,  and  sell  them 
for  $375,  what  do  I  gain  per  cent.  ? 

5.  Mr.  C.  bought  a  horse  for  $153,  and  sold  him 
for  $128  ;  what  per  cent,  did  he  lose  ? 

6.  A  grocer  bought  eggs  for  9  cents  a  dozen,  and 
sold  them  for  12  cents  ;  what  per  cent,  did  he  gain  ? 

7.  What  per  cent,  is  lost  in  buying  corn  at  50 
cents  a  bushel,  and  selling  it  at  45  cents  ? 

8.  If  a  house  bring  |-  of  its  value  every  4  years  in 
rent,  what  is  the  gain  per  cent,  each  year  ? 

9.  Bought  a  horse  for  20  per  cent,  less  than  $150, 
and  sold  him  for  10  per  cent  more  than  $150  ;  what 
per  cent,  was  gained  ? 

10.  A  peddler  bought  oranges  for  18  cents  a  dozen, 
and  sold  them  for  2  cents  each  ;  what  per  cent,  did 
he  gain  ? 

11.  A  farmer  refused  to  sell  his  barley  for  75 
cents  a  bushel,  and  was  afterwards  obliged  to  take 
60  cents  a  bushel  for  it ;  what  per  cent,  did  he  lose  ? 

12.  Bouglit  cotton  cloth  at  7-|-  cents  a  yard,  and 
sold  it  for  9  cents  a  yard  ;  wha"t  was  the  gain  per 
cent.  ? 

13.  Sold  damaged  cloth  so  as  to  lose  J  of  what  it 
cost ;  what  per  cent,  was  lost  ? 


126  INTELLECTUAL   ARITHMETIC.  [84. 

84.  1.  A  tailor  sold  a  coat  for  124,  b J  whicli  he 
gained  20  per  cent,  on  the  first  cost ;  what  was  its 
cost  ? 

Analysis.  Since  he  gained  20  per  cent,  or  ^  of  the 
cost,  l^'l^  is  f  of  the  cost ;  since  $24  is  f,  ^  o/$24,  or  $4, 
is  -^  of  the  cost,  and  $4  is  i  of  6  times  $4,  or  $20.  There- 
fore, S^c» 

2.  A  hatter  sold  a  hat  for  $3-J-,  which  was  12J- 
per  cent,  above  cost ;  what  did  it  cost  : 

3.  A  jeweler  sold  a  watch  for  $Q5,  thereby  gain- 
ing 30  per  cent,  on  its  cost ;  what  was  its  cost  ? 

4.  A  mechanic  sold  a  carriage  for  $108,  which 
was  10  per  cent,  less  than  it  cost ;  how  much  would 
he  have  received  for  it  had  he  sold  it  so  as  to  gain 
20  per  cent.  ? 

5.  If  16|  per  cent,  is  gained  by  selling  flour  at 
$1  a  barrel,  what  did  it  cost  ? 

6.  A  merchant  sold  2  barrels  of  sugar  for  $24 
each  ;  on  one  barrel  he  gained  20  per  cent,  and  on 
the  other  he  lost  20  per  cent.  ;  did  he  gain  or  lose 
by  the  bargain,  and  how  much  ? 

7.  A  grocer  bought  coffee  so  that  he  could  sell  it 
for  18  cents  a  pound,  and  make  a  profit  of  33-^-  per 
cent.  ;  what  did  it  cost  him  ? 

8.  A  man  bought  a  horse  and  carriage ;  he  sold 
them  both  at  8  per  cent,  above  cost,  receiving  $81 
for  the  horse,  and  $108  for  the  carriage  ;  what  was 
the  cost  of  both  ? 

9.  A  fruit  dealer  sold  pine-apples  at  96  cents  a 
dozen,  thereby  losing  4  per  cent. ;  what  did  they  cost 
apiece  ? 

10.  B  sells  a  horse  to  C,  and  gains  12|-  per  cent. ; 
C  sells  him  to  D  for  $118,  and  thereby  gains  18  per 
cent. ;  how  much  did  the  horse  cost  B  ? 


85.]  INTELLECTUAL   ARITHMETIC.  127 

8d.  1.  Sold  Avheat  so  as  to  gain  16  cents  on  a 
bushel,  which  was  12|-  per  cent,  of  what  it  cost ;  what 
did  it  cost  ? 

2.  A  broker  exchanged  $150  at  ^  per  cent.  ;  how 
much  brokerage  did  he  receive  ? 

3.  A  man,  having  a  farm  of  200  acres,  sold  75 
acres  of  it;  what  per  cent,  of  the  whole  remains 
unsold  ? 

4.  What  per  cent,  does  William  gain  by  selling 
apples  at  |-  of  the  cost  ? 

5.  If  I  buy  stoves  at  $12  each,  and  sell  them  at 
S^  per  cent,  profit,  what  Avill  I  gain  on  1  stove  ? 

6.  If  a  broker  buy  $800  worth  of  bank  stock  for 
me,  and  charge  ^  per  cent,  brokerage,  how  much 
will  he  receive  ? 

7.  Sold  butter  so  as  to  gain  |  as  much  as  it  cost ; 
what  per  cent,  was  gained  ? 

8.  Mr.  A.  lends  his  money  so  as  to  receive  a  sum 
equal  to  -^q  of  it  for  its  use ;  Avliat  per  cent,  does  he 
receive  ? 

9.  A  brewer  sends  a  person  $520  with  which  to 
purchase  barley,  after  deducting  his  commission  of  4 
per  cent. ;  how  much  does  he  expend,  and  how  much 
does  his  commission  amount  to  ? 

10.  The  cost  of  building  a  town  house,  and  paying 
collector's  fees  of  5  per  cent.,  was  $945  ;  what  was  the 
cost  of  the  house  ? 

11.  Hiram  agrees  to  dig  farmer  F.'s  potatoes  for 
8  per  cent,  of  what  should  be  put  into  the  farmer'^ 
cellar ;  he  digs  324  bushels ;  how  many  bushels 
should  be  put  into  the  cellar,  and  how  many  bushels 
should  Hiram  receive  ? 

12.  Bought  $200  worth  of  dry  goods,  and  $300 
worth  of  groceries  ;  on  the  dry  goods  I  lost  20  per 
cent.,  but  on  the  groceries  I  gained  15  per  cent. ;  did 
I  gain  or  lose  on  my  whole  capital,  and  how  much  ? 


128  INTELLECTUAL   ARITHMETIC.  [85. 

13.  A  merchant  bought  40  bushels  of  grass  seed, 
at  the  rate  of  4  bushels  for  $6,  and  sold  it  at  the 
rate  of  5  bushels  for  $8 ;  what  was  his  whole  gain, 
and  what  his  gain  per  cent.  ? 

14.  A  drover  bought  20  sheep  for  $50,  and  sold 
them  so  as  to  gain  20  per  cent. ;  how  much  did  he 
receive  a  head  for  them  ? 

15.  A  man  bought  60  cords  of  wood  for  |200, 
and  sold  it  at  a  loss  of  5  per  cent. ;  at  what  price 
did  he  sell  it  per  cord  ? 

18.  If  I  buy  rice  at  4  cents  a  pound,  and  sell  it 
at  5  cents,  what  is  my  gain  per  cent.  ? 

17.  Sold  a  cow  at  auction  for  $18  that  cost  $20 ; 
what  was  the  loss  per  cent.  ? 

18.  A  boy  bought  peaches  at  the  rate  of  3  for  2 
cents,  and  sold  them  at  the  rate  of  9  for  7  cents, 
what  was  his  gain  per  cent.  ? 

19.  A  tailor  sold  two  coats  for  $26  each ;  on  one 
he  gained  30  per  cent.,  and  on  the  other  he  lost 
30  per  cent. ;  did  he  gain  or  lose  on  both,  and  how 
much  ? 

20.  A  music  dealer  sold  a  piano-forte  for  $230, 
which  was  8  per  cent,  less  than  its  value ;  had  he 
sold  it  for  $300,  what  Avould  have  been  his  gain  per 
cent.  ? 

21.  Two  men  buy  a  lot  of  pork  together ;  A  fur- 
nishes $200,  and  B  $150 ;  their  profits  are  $70 ;  what 
is  their  gain  per  cent.,  and  what  is  each  one's  share 
of  the  gain  ? 

22.  If  a  ton  of  hay  is  bought  for  |  of  the  market 
price,  and  sold  for  5  per  cent,  more  than  the  market 
price,  what  per  cent,  is  gained  ? 

23.  A  person  engaged  in  speculation  sold  out  his 
interest  for  $2100,  which  was  30  per  cent,  less  than 
twice  as  much  money  as  he  began  with ;  how  much 
did  he  begin  with,  and  what  was  his  gain  ? 


§0,]  INTELLECTUAL  ARITHMETIC.  129 

§@,  Interest  is  a  sum  paid  for  the  use  of  borrowed 
money,  or  on  demands  after  they  become  due. 

The  PiiiNCiPAL  is  the  money  lent,  or  the  sum  for  which 
interest  is  paid. 

The  Amount  is  the  sum  of  the  principal  and  interest. 

The  Rate  per  Cent,  is  the  sum  paid  for  the  use  of 
SlOO  or  100  cents  for  one  year.  Thus,  if  $6  be  paid  for 
the  use  of  $100  one  year,  the  rate  is  6  per  cent,  per 
annum. 

The  interest  on  any  sum  for  one  year  is  always  a  certain 
number  of  hundredths  of  the  principal.  Thus,  the  interest 
of  any  sum  for  one  year,  at  5  per  cent.,  is  5  hundredths 
(tub)  or  ^V  of  the  principal ;  at  8  per  cent,  it  is  8  hun- 
drcdtiLS  (xf  xr)  or  -^-^  of  the  principal. 

Practically.,  SO  days  are  considered  a  month,  and  12 
months  a  year,  in  computing  interest.  When  no  time  is 
named,  one  year  is  always  understood. 

The  rate  of  interest  is  established  by  law;  and  taking 
more  than  such  rates  is  termed  usury. 

1.  What  is  the  yearly  interest  of  ^80,  at  5  per  cent.  ? 

Analysis.  Sinc^.  the  interest  is  5  per  cent.,  or  y^^,  equal 
to  -'^  of  the  princ^'pal,  the  interest  of  $80  is  -^\y  of  $80, 
or  $4.      Therefore,  SfC. 

Or  tlius  :  Siy^ne  the  interest  of  $1,  or  100  cents,  is  5  cents 
for  one  year,  the  interest  of  $80  is  80  twies  5  cents,  or  400 
cents,  equal  to  $4.* 

2.  What  is  the  yearly  interest  of  $200,  at  6  per 
cent.  ? 

3.  What  is  the  yearly  interest  of  $125,  at  4  per 
cent.  ? 

4.  What  is  the  annual  interest  of  $80,  at  7  per 
cent.  ? 

5.  What  is  tho  annual  interest  of  $95,  at  5  per 
cent.  ? 

*  The  fractio'Hf^  method  is  considered  preferable  in  mental  exercises. 
9 


130  INTELLECTUAL   ARITHMETIC.  [87. 

6.  What  is  the  annual  interest  of  $26,  at  10  per 
cent.  ? 

7.  What  is  the  annual  interest  of  |228,  at  12|- 
per  cent.  ? 

8.  What  is  the  annual  interest  of  196.32,  at  6| 
per  cent.  ? 

9.  What  is  the  annual  interest  of  8144.60,  at  8J 
per  cent.  ? 

10.  What  is  the  annual  interest  of  $400,  at  15 
per  cent.  ? 

11.  What  is  the  annual  interest  of  $500,  at  7 
per  cent.  ? 

12.  What  is  the  annual  interest  of  1120.80,  at  7| 
per  cent.  ? 

13.  What  is  the  annual  interest  of  $1000,  at  9 
per  cent.  ? 

14.  What  is  the  annual  interest  of  $150,  at  3  per 
cent.  ? 


87.  1.  What  is  the  interest  of  $150  for  3  years, 
at  8  per  cent.  ? 

Analysis.  Since  the  interest  for  1  year  at  8  per  cent, 
is  jf^,  equal  to  ^2_,  of  the  principal,  for  3  years  it  is  3 
times  4^,  or  -S^,  of  the  principal.  ^^  ^f  ^^^^  **  ^^j  ^"^ 
^6-  o/*'$150  Is  6  times  $6,  or  $36.      Therefore,  Sfc. 

Or  thus  :  Siiice  the  interest  of  $150  for  1  year  at  8  per 
cent,  is  $12,  (86,)  for  3  years  it  is  3  times  $12,  or  $36. 

2.  What  is  the  interest  of  $30  for  2  years,  at  5 
per  cent.  ? 

3.  What  is  the  irnterest  of  $50  for  4  years,  at  6 
per  cent.  ? 

4.  What  is  the  interest  of  $90  for  5  years,  at  7 
per  cent.  ? 

5.  What  is  the  interest  of  $75  for  3  years,  at  12 
per  cent.  ? 


88.]  INTELLECTUAL   ARITHMETIC.  131 

6.  What  is  the  interest  of  864.96  for  2  years,  at 
6|  per  cent.  ? 

7.  A's  note  of  |25  has  been  due  2  years  ;  what  is 
the  interest,  at  6  per  cent.  ? 

8.  Borrowed  8-300  for  3  years,  at  7  per  cent. ; 
what  will  be  the  interest  ? 

9.  What  is  the  interest  on  a  note  of  $16.50,  for  5 
years,  at  10  per  cent.  ? 

10.  I  owe  two  notes,  one  for  8145,  due  in  2  years, 
at  5  per  cent.,  and  the  other  for  8200,  due  in  3  years, 
at  6  per  cent. ;  what  will  be  the  sum  of  the  interest 
that  I  must  pay  ? 

11.  What  is  the  interest  of  8225  for  2  years,  at  7 
per  cent.  ? 

12.  What  is  the  interest  of  850  for  8  years,  at  6 
per  cent.  ? 

13.  What  is  the  interest  of  8400  for  2  years,  at 
5J-  per  cent.  ? 

"14.    Gave  a  note  for  888.96,  due  in  3  years,  at  6| 
per  cent ;  what  will  be  the  interest  ? 

15.  Gave  a  note  due  at  date,  for  845.50,  but  did 
not  pay  it  until  the  end  of  5  years ;  what  was  the 
interest  due,  at  8  per  cent.  ? 


88.  1.  At  8  per  cent.,  what  part  of  81  equals 
the  use  of  it  for  3  years  9  months  ? 

Analysis.  Since  there  are  12  months  in  1  year^  9 
months  is  y^^*  or  ^  of  \  year,  and  3  years  9  months  are  equal 
to  3|^,  or  ■'^-^-  years.     Since   the   interest  of  %\  for  1  year  at 

8  per  cent,  is  y^^y,  equal  to  ^t;  of  the  principaU  for  3  years 

9  months,  it  is   3|-   ti?nes,  or  -y^-,  of  -^^^  equal  to  -^^  of  the 
principal^  or  %y^.      Therefore,  ^-c. 

2.  At  6  per  cent.,  what  part  of  81  equals  the  use 
of  it  for  2  years  8  months  ? 


132  INTELLECTUAL   AEITHMETIC.  [88. 

3.  At  5  per  cent.,  what  part  of  any  sum  equals 
the  use  of  it  for  2  years  6  months  ? 

4.  At  7  per  cent.,  what  part  of  any  sum  equals 
the  interest  of  it  for  1  year  8  months  ? 

5.  What  part  of  any  sum  equals  the  interest  of  it 
for  3  years  2  months,  at  4  per  cent.  ? 

6.  What  part  of  any  sum  equals  the  interest  of  it 
for  5  years  4  months,  at  9  per  cent.  ? 

7.  At  6^  per  cent.,  for  3  years  4  months,  what 
part  of  the  interest  equals  the  principal  ? 

8.  At  8  per  cent.,  for  5  years  5  months,  what  part 
of  the  principal  equals  the  interest  ? 

9.  At  7^-  per  cent.,  for  2  years  11  months,  what 
part  of  the  principal  equals  the  interest  ? 

10.  At  6  per  cent.,  for  2  years  1  month,  what  part 
of  the  principal  equals  the  interest  ? 

11.  At  10  per  cent.,  for  4  years  10  months,  what 
part  of  the  principal  equals  tlie  interest  ? 

12.  At  8  per  cent.,  for  3  years  3  months  and  18 
days,  what  part  of  the  principal  equals  the  interest  ? 

Analysts.  Since  30  days  make  a.  month,  18  days  are 
4^8.,  or  ^  of  a  month  ;  and  since  12  months  make  a  year, 
1  month  is  yV  of  a  year ;  ^  of  1  month  is  ^  of  yV, 
or  ^\j  of  1  year,  and  3|  months,  equal  to  ^^-,  is  18  times  -^^j, 
or  y^^  of  a  year.  Hence  the  interest  of  $1  for  Sy^^y,  or  ^^ 
years,  at  8  per  cent.,  is  y^^\  of  it.  (8Sj  Ex.  1.)  There* 
fore,  ^c. 

13.  What  part  of  the  principal  equals  the  inter- 
est, for  2  years  5  months  and  10  days,  at  6  per  cent.  ? 

14.  Wliat  part  of  the  principal  equals  the  interest, 
for  1  year  8  months  and  25  days,  at  7  per  cent.  ? 

15.  What  part  of  the  iH'incipal  equals  the  interest, 
for  2  years  3  months  and  6  days,  at  6  per  cent.  ? 

16.  What  part  of  the  principal  equals  the  interest, 
for  2  years  11  months  and  6  days,  at  5  per  cent^  ? 


89.]  INTELLECTUAL   ARITHMETIC.  133 

17.  At  7|-  per  cent.,  for  8  months  10  days,  v/liat 
part  of  the  principal  will  equal  the  interest  ? 

18.  At  6  per  cent.,  for  5  years  7  months  and  15 
days,  ^vhat  part  of  the  principal  will  equal  the 
interest  ? 

19.  At  8 J  per  cent.,  for  3  years  5  months  and 
12  days,  what  part  of  the  principal  equals  the  in- 
terest V 

20.  At  7  per  cent.,  for  11  months  3  days,  what 
part  of  the  principal  will  equal  the  interest  ? 

21.  At  4  per  cent.,  for  8  years  6  months  and  15 
days,  what  part  of  the  principal  will  equal  the  in- 
terest ? 


§9,  1.  What  is  the  interest  of  840  for  3  years 
4  months,  at  6  per  cent.  ? 

Analysis.  3  years  4  months  equals  3^,  or  ^^-  years  ; 
and  the  interest  of  any  sum  for  ^^-  years,  at  6  j^e?'  cent.^ 
equals  ^  of  it.  (88.)  -5-  of  $40  is  $8,  the  required  in^ 
terest.      Therefore,  ^c. 

Or  thus :  Since  the  interest  of  $1  for  1  year,  at  G  per 
cent.,  is  6  cents,  for  $40  it  is  40  times  6  cents,  or  $2.40,  and 
for  3^  years  it  is  3^-  times  $2.40,  equal  to  $8. 

2.  What  is  the  interest  of  8150  for  2  years  10 
months,  at  8  per  cent.  ? 

3.  What  is  the  interest  of  880.40  for  4  years  2 
months,  at  7  per  cent.  ? 

4.  What  is  the  interest  of  8240  for  1  year  9 
Months,  at  5  per  cent.  ? 

5.  What  is  the  interest  of  8120  for  5  years  8 
months,  at  1\  per  cent.  ? 

6.  What  is  the  interest  of  890  for  4  years  7 
months,  at  4  per  cent.  ? 

7.  What  is  the  interest  of  8500  for  10  months,  at 
6  per  cent.  ? 


134  INTELLECTUAL   APJTHMETIC.  l& 

8.  What  is  the  interest  of  $128  for  2  years  9 
months,  at  6|-  per  cent.  ? 

9.  What  is  the  interest  of  $125  for  1  year  4 
months,  at  7  per  cent.  ? 

10.  What  is  the  interest  of  |300  for  8  months,  at 
6  Der  cent.  ? 

11.  What  is  the  interest  of  |50  for  5  years  7 
months  and  15  days,  at  8  per  cent.  ? 

Analysis.  The  interest  of  any  sum  for  5  years  7  months 
and  15  days,  at  8  per  cent.,  equals  -^^  of  it,  (885  Ex.  12  ;) 
2-V  of  $50  is  $2^,  and  ^%  of  $50  is  9  times  $2^-,  equal  to 
$22i.      Therefore,  ^c. 

12.  What  is  the  interest  of  175.60  for  4  years  5 
months  and  10  days,  at  9  per  cent.  ? 

13.  What  is  the  interest  of  $50  for  6  years  4 
months  and  24  days,  at  5  per  cent.  ? 

14.  What  is  the  interest  of  $300  for  4  years  7 
months  and  15  days,  at  8  per  cent.  ? 

15.  What  is  the  interest  of  $288  for  8  months  10 
days,  at  7  J  per  cent.  ? 

16.  What  is  the  interest  of  $1200  for  20  days,  at 
6  per  cent.  ? 

17.  What  is  the  interest  of  $40  for  9  months  5 
days,  at  4^-  per  cent.  ? 

18.  Wiiat  is  the  interest  of  $36.72  for  5  years  6 
months  and  20  days,  at  7  per  cent.  ? 

19.  Wliat  is  the  interest  of  $120  for  2  years  1 
month  and  6  days,  at  12|-  per  cent.  ? 

20.  What  is  the  interest  of  $24  for  11  months  and 
20  days,  at  15  per  cent.  ? 

21.  What  is  the  interest  of  $2000  for  18  days,  at 
5  per  cent.  ? 

22.  What  is  the  interest  of  $1500  for  2  months 
and  24  days,  at  6  per  cent.  ? 


,]  INTELLECTUAL   ARITHMETIC.  135 


1.    Yvliat  will  be  the  amount  of  $60  for  2 
years  6  months,  at  6  per  cent.  ? 

Analysis.  Since  the  interest  is  equal  to  ^^^  of  the  prin- 
cipal^ (^^5)  and  the  amount  is  equal  to  the  principal  and 
interest,  it  folloivs  that  %%,  the  principal,  added  to  ^^g-,  the 
interest,  equals  §3',  ^^^^  amount,  ^^u"  ^f  ^^^  is  $3,  arid  f  ^- 
of  $60  is  23  times  $3,  or  $69,  the  amouyit.     Therefore,  ^c, 

Note.    "When  more   convenient,  the  interest  may  first  be  found,  to 
which  add  the  principal,  and  the  result  will  be  the  amount. 

2.  What  is  the  amount  of  $36  for  4  years  2 
months,  at  7  per  cent.  ? 

3.  What  will  $120  amount  to  in  2  years  11 
months,  at  8  per  cent.  ? 

4.  What  will  $96.48  amount  to  in  3  years  4 
months,  ac  6^  per  cent.  ? 

5.  What  will  $80.50  amount  to  in  6  years  8 
months,  at  4|  per  cent.  ? 

6.  What  will  $20.25  amount  to  in  12  years,  at  5 
per  cent.  ? 

7.  What  will  $1500  amount  to  in  10  months,  at 
10  per  cent.  ? 

8.  What  will  $150  amount  to  in  6  months  and  20 
days,  at  6  per  cent.  ? 

9.  What  will  $250  amount  to  in  9  months  and  18 
days,  at  7^  per  cent.  ? 

10.  What  is  the  amount  of  $480  for  1  year  10 
months  and  25  days,  at  5  per  cent.  ? 

11.  What  is  the  amount  of  $500  for  3  years  4 
months  and  24  days,  at  6  per  cent.  ? 

12.  What  is  the  amount  of  $240  for  2  years  7 
months  and  6  days,  at  7  per  cent.  ? 

13.  What  is  the  amount  of  $1000  for  5  years  1 
month  and  6  days,  at  4  per  cent.  ? 

14.  What  is  the  amount  of  $120  for  10  years  6 
months  and  20  days,  at  3  per  cent.  ? 


136  INTELLECTUAL   ARITHMETIC.  [91. 


1.    What  principal  in  3  years  9  months,  at 
8  per  cent.,  will  give  $90  interest  ? 

Analysis.  Since  the  interest  for  3  years  9  months,  at  8 
per  cent.,  is  -^^  of  the  principal,  (S85)  $90  must  be  -^-q-  of 
the  required  principal.  Since  $90  is  y^^,  ^tt  is  ^  o/$90jO/ 
$30,  and  $30  is  y^  of  10  times  $30,  or  $300,  the  principal 
Therefore,  S)-c. 

2.  What  principal,  in  1  year  8  months,  at  9  per 
cent.,  will  give  836  interest? 

8.  What  principal  in  11  months,  at  6  per  cent., 
will  give  $22  interest  ? 

4.  What  principal  in  7  months  15  days,  at  8  per 
cent.,  Avill  give  $40  interest? 

5.  A  rents  a  store  to  B  for  the  yearly  rent  of  $300, 
which  is  12  per  cent,  of  its  cost ;  what  did  it  cost  ? 

6.  A  gentleman  bonght  6  horses,  for  which  he  paid 
a  sum  of  money  which  in  2  years  6  months,  at  4  per 
cent.,  would  have  given  him  $90  interest;  what  did 
he  pay  apiece  for  the  horses  ? 

7.  A  person  deposits  |  of  his  money  in  the  bank, 
which  brings  him  an  annual  income  of  $1500,  at  10 
per  cent. ;  the  remaining  |  he  invests  in  business 
which  yields  him  20  per  cent,  profit ;  what  are  his 
entire  capital  and  his  yearly  income  ? 

8.  Two  persons  engaged  in  trade  ;  A  furnished  | 
of  the  capital,  and  B  | ;  at  the  end  of  3  years  and  4 
months  they  found  that  they  had  made  a  clear  profit 
of  $5000,  which  is  12^^  per  cent,  per  annum  on  the 
money  invested  ;  how  much  capital  did  each  furnish  ? 

9.  A  capitalist  invested  |  of  his  money  in  railroad 
stock,  which  depreciated  5  per  cent,  in  value ;  the 
remaining  |  he  invested  in  bank  stock,  which  at  the 
end  of  1  year  had  gained  $1200,  which  was  12  per 
cent,  of  the  investment ;  what  was  the  whole  amount 
of  his  capital,  and  what  was  his  entire  loss  or  gain  ? 


SJ3.]  INTELLECTUAL   ARITHMETIC.  137 

92,  1.  What  principal  will,  in  3  years  4  months, 
at  5  per  cent,  amount  to  $700. 

Analysis.  Since  the  interest  for  3  years  4  months,  at  5 
per  cent.,  is  ^  of  the  principal,  (88,)  the  principal  |,  added 
to  the  interest  ^,  equals  the  amount  \ ;  hence  $700  is  \  of 
the  principal  Since  $700  is  f,  ^  is  }  of  $700,  or  $100, 
and  $100  is  ^  of  6  times  $100,  or  $600.      Therefore,  ^c. 

2.  What  principal  in  5  years,  at  6  per  cent.,  will 
amount  to  $1300  ? 

3.  What  principal  in  1  year  6  months,  at  8  per 
cent.,  will  amount  to  $280  ? 

4.  What  principal  in  4  years  2  months,  at  3  per 
cent.,  will  amount  to  $630  ? 

5.  What  principal  in  10  years,  at  7  per  cent.,  will 
amount  to  $340  ? 

6.  What  principal  in  9  months,  at  10  per  cent., 
will  amount  to  $172  ? 

7.  What  principal  in  18  months,  at  4  per  cent., 
will  amount  to  $530  ? 

8.  The  amount  due  on  a  bond  and  mortgage  is 
$2900,  it  having  been  on  interest  7  years  6  months, 
at  6  per  cent.  ;  what  was  the  principal  ? 

9.  Two  men  bought  200  acres  of  land,  and  at  the 
end  of  2  years  sold  it  for  $1500,  which  was  an  ad- 
vance of  12^  per  cent,  per  annum  on  its  cost ;  what 
did  it  cost  an  acre  ? 

10.  A  man  invested  J  of  all  he  was  worth  in  the 
lumber  trade,  and  at  the  end  of  2  years  8  months 
sold  out  his  entire  interest  for  $3100,  whicli  was  a 
yearly  gain  of  9  per  cent,  on  the  money  invested  ;  how 
much  was  he  worth  vrhen  he  commenced  trade  ? 

11.  A's  money  is  to  B's  as  2  to  3  ;  if  J  of  A's 
money  be  put  at  interest  for  3  years  9  months,  at 
10  per  cent.,  it  will  amount  to  $550  ;  how  much 
money  has  each  ? 


188  INTELLECTUAL   ARITHMETIC.  [93. 

9S.     1.    Ill  what  time,  at  5  per  cent.,  will  |60 

gain  $15  interest  ? 

Analysis.  77^6  gain,  or  interest,  is  ^^-,  or  ^  of  the  prin- 
cipal, equal  to  25  per  cent,  of  the  principal.  (7T^  Ex.  7.) 
Jf  a  given  principal  gain  5  per  cent,  in  1  year,  it  will  re- 
quire as  many  years  to  gain  25  per  cent,  as  5  per  cent,  is 
contairied  times  in  25  per  cent.,  or  5  years.      Therefore,  ^c. 

Or  thus :  Since  $60  in  1  year,  at  5  per  cent.,  will  gain 
S3  interest,  it  will  require  as  many  years  for  $60  to  gain 
$15  interest,  as  $3  is  contained  times  in  $15,  which  is  5 
times. 

2.  How  long  will  it  take  $120  to  gain  |24  interest, 
at  6  per  cent.  ? 

3.  In  what  time  will  $500  gain  $35,  at  7  per 
cent.  ? 

4.  In  what  time  will  $120  gain  $40,  at  10  per 
cent.  ? 

5.  In  what  time  will  $80  gain  $6,  at  3  per  cent.  ? 

6.  In  what  time  will  $300  gain  $84,  at  7  per 
cent.  ? 

7.  In  what  time  will  $160  gain  $20,  at  6^  per 
cent.  ? 

8.  In  what  time  will  $49  gain  $12.25,  at. 5  per 
cent.  ? 

9.  In  what  time  will  any  given  principal  douhle 
itself  at  4  per  cent.  ? 

Analysis.  Since,  to  douhle  itself,  any  sum  of  money 
must  gain  100  per  cent.,  at  1  per  cent.,  it  loill  require  100 
years,  at  4  per  cent.,  ^  of  100  years,  or  25  years.  There- 
fore, ^'C. 

10.  In  what  time  will  a  given  principal  double  it- 
self at  5  per  cent.  ? 

11.  In  what  time  will  a  given  principal  double  it- 
self at  7  per  cent.  ? 


94.]  INTELLECTUAL   ARITHMETIC.  ISO 

12.  In  what  time  will  a  given  principal  double  it- 
self at  6  per  cent.  ? 

13.  In  what  time  will  a  given  principal  double  it- 
self at  10  per  cent.  ? 

14.  In  what  time  will  1500  double  itself,  at  12J 
per  cent.  ? 

15.  In  what  time  will  |175  double  itself  at  20  per 
cent.  ? 

16.  In  what  time  will  a  given  principal  treble  it- 
self at  5  per  cent.  ? 

Analysis.  A  given  principal  ivill  treble  itself  at  1  per 
cent,  in  200  years  ;  at  5  per  cent,  in  \  of  200  years,  or  40 
years, 

17.  In  what  time  will  8100  treble  itself  at  6  per 
cent.  ?  at  7  per  cent.  ?  at  8  per  cent.  ?  at  10  per 
cent.  ? 


1^4.  1.  A  man  loaned  875  for  4  years,  and  re- 
ceived $18  interest ;  what  was  the  rate  per  cent.  ? 

Analysis.  Since  tlic  gain,  or  interest^  for  4  years,  is 
rh  ^^  i^b  ^f  ^^'^  principal,  for  1  year  it  is  ^  of  ^^,  or  ^fg- 
of  the  principal,  equal  to  6  per  cent.      Therefore,  ^c. 

Or,  thus  :  At  1  per  cent.,  the  interest  of  $1  for  4  years  is 
4  ce?its,  and  of  $75  it  is  75  times  4  cents,  which  are  300 
cents,  equal  to  $3.  Since  $3  interest  is  1  per  cent,  of  $75 
for  4  years,  $18  interest  is  as  many  per  cent,  as  $3  is 
contained  times  in  $18,  which  is  6  times,  equal  to  G  per 
cent. 

2.  At  what  per  cent,  will  $200  gain  $49  interest 
in  3|-  years  ? 

3.  At  what  per  cent,  will  $60  gain  $25  interest  in 
4J  years  ? 

4.  At  what  per  cent,  will  $90  gain  $27  in  6 
years  ? 


140  INTELLECTUAL   ARITHMETIC. 

5.  At  what  per  cent,  will  $12  gain  $5  in  10 
years  ? 

6.  At  what  per  cent,  will  $400  gain  $55  interest 
in  2|-  years  ? 

7.  At  what  per  cent,  will  $150  gain  $44  interest 
in  3|  years  ? 

8.  At  what  per  cent,  will  $125  gain  $37.50  interest 
in  5  years  ? 

9.  At  what  per  cent,  will  $800  gain  $75  interest 
in  1  year  and  3  months  ? 

10.  At  what  per  cent,  will  $180  gain  $45  interest 
in  3  years  and  9  months  ? 

11.  At  what  per  cent,  will  $1250  gain.  $312.50 
interest  in  2  years  6  months  ? 

12.  At  what  per  cent,  will  $2500  gain  $200  in- 
terest in  1  year  and  4  months  ? 

13.  At  what  per  cent,  will  a  given  principal  double 
itself  in  5  years  ? 

Analysis.  Since  a  given  principal  must  gain  100  per 
cent,  to  double  itself  in  1  year,  to  double  itself  in  5  years  ivill 
require  ^  of  100  per  cent.,  or  20  per  cent.      Therefore,  SfC. 

14.  At  what  per  cent,  will  a  given  principal  double 
itself  in  10  years  ? 

15.  At  what  per  cent,  will  a  given  principal  double 
itself  in  12  years  6  months  ? 

16.  At  what  per  cent.  Avill  $200  double  itself  in  4 
years  ? 

17.  At  what  per  cent,  will  $100  double  itself  in  8 
years  ? 

18.  At  what  per  cent,  will  $150  double  itself  in 

15  years  ? 

19.  At  what  per  cent,  will  $300  double  itself  in 

16  years  8  months  ? 

20.  At  what  per  cent,  will  $175  double  itself  in 
2  years  6  months  ? 


95>.]  INTELLECTUAL   ARITHMETIC.  141 

05.  The  2^^'<^sent  worth  of  a  note  payable  a*:  a  future 
time  is  such  a  sum  a?,  put  at  interest  at  the  given  rate  per 
cent,  until  it  becomes  due,  will  amount  to  the  face  of  the 
note. 

Discount  is  an  allowance  made  for  the  payment  of  money 
before  it  becomes  due,  and  is  obtained  by  subtracting  the 
■present  worth  from  the  given  sum  or  face  of  the  note. 

1.  What  is  the  present  worth  of  $180  payable  in 
8  years  4  months  at  6  per  cent,  'i 

Analysis.  Since  the  interest  for  3  years  4  months  at 
6  per  cent,  is  \  of  the  principal,  (^^j)  ^^^^  amount,  $180, 
is  equal  to  the  principal,  |^,  added  to  the  interest,  \,  equal  to 
f  of  the  principal.  Since  $180  is  f  of  the  principal,  ^  of 
$180,  or  $30,  is  \,  and  $30  is  \  of  5  times  $30,  or  $150. 
Therefore,  SfC. 

Note.    The  discount  is  the  difference  between  ^180  and  $150,  which 
is  $30. 

2.  What  is  the  present  worth  of  a  note  for  $36.90, 
payable  in  2  years  6  months,  at  5  per  cent.  ? 

3.  What  is  the  present  value  of  a  note  for  854, 
due  in  5  years,  and  bearing  interest  at  7  per  cent.  ? 

4.  What  is  the  present  value  of  a  debt  of  8124.40, 
due  in  4  years  2  months,  at  8  per  cent,  interest  ? 

5.  What  is  the  discount  of  82100,  due  in  1  year 
3  months,  at  4  per  cent.  ? 

6.  What  is  the  discount  on  a  note  of  8560,  paya- 
ble in  2  years,  at  6  per  cent,  interest  ? 

7.  What  is  the  difference  between  the  interest  and 
the  discount  of  8130,  due  10  months  hence,  at  10 
per  cent.  ? 

8.  A  man,  having  a  span  of  horses  for  sale,  offered 
them  for  8480  cash  in  hand,  or  a  note  of  8550  due 
in  1  year  8  months  without  interest.  The  buyer 
accepted  the  latter  offer  ;  did  the  seller  gain  or  lose 
by  his  offer,  and  how  much,  allowing  the  money  to 
be  worth  6  per  cent.  ? 


142  INTELLECTUAL   ARITHMETIC.  [S$6. 


1.    B  sold  a  horse  for  |   of  1|  times  the 
cost ;  what  was  the  gain  per  cent.  ? 

2.  A  cow  purchased  for  ^28  in  the  spring  was  sold 
for  $21  in  autumn  ;  what  was  the  loss  per  cent.  ? 

3.  An  old  lady  bought  80  apples  of  John  at  the 
rate  of  2  for  a  cent,  as  many  more  of  William  at  the 
rate  of  3  for  a  cent,  and  sold  the  whole  at  the  rate 
of  5  for  2  cents  ;  did  she  gain  or  lose,  and  at  what 
rate  per  cent.  ? 

4.  Did  she  gain  or  lose  on  the  purchase  made  of 
John  or  William,  and  at  v/hat  rate  per  cent,  on  the 
amount  of  the  purchase  ? 

5.  A  hogshead  of  molasses  was  bought  for  $20 ; 
11-J  per  cent,  of  it  leaked  out ;  how  must  the  re- 
mainder be  sold  per  gallon  to  gain  40  per  cent,  on 
the  cost  ? 

6.  A  manufacturer  sold  2  machines  for  $391  each  ; 
on  one  he  gained  15  per  cent.,  on  the  other  he  lost 
15  per  cent. ;  did  he  gain  or  lose  on  the  sale  of  both, 
and  how  much  ? 

7.  How  much  wheat  must  be  taken  to  mill,  that 
6  bushels  may  be  retained  after  giving  toll  of  6 
pounds  per  bushel,  or  10  per  cent,  for  grinding  ? 

8.  A  man  brought  home  1500  feet  of  lumber  after 
giving  37  J  per  cent,  of  the  whole  for  sawing ;  how 
much  lumber  did  he  have  sp.wod  ? 

9.  A  farmer  sold  2  horses  for  $150  apiece  ;  on  one 
he  gained  25  per  cent.,  on  the  other  he  lost  25  per 
cent. ;  did  he  gain  or  lose  on  both,  and  how  much  ? 

10.  For  hulling  barley,  36  per  cent,  is  taken  for 
pay ;  at  this  rate,  how  many  bushels  must  be  taken 
that  32  bushels  be  returned  after  hulling  ? 

11.  In  a  school  district  $57  was  to  be  collected 
for  teacher's  wages  ;  the  collector  was  to  have  5  per 
cent,  on  all  moneys  collected  ;  how  much  must  he 
collect  to  pay  his  fee  and  the  teacher  ? 


96.]  INTELLECTUAL   ARITHMETIC.  143 

12.  How  much  plaster  must  A  have  ground,  to 
bring  home  14  tons,  after  the  miller  has  taken  12^- 
per  cent,  of  all  he  has  ground  ? 

13.  In  how  many  years,  at  5  per  cent.,  will  a 
given  principal  amount  to  the  same  as  it  would  at  7 
per  cent,  in  3  years  ? 

14.  At  what  rate  per  cent,  in  12  years  will  a  given 
principal  amount  to  the  same  as  at  7  per  cent,  for  8 
years  ? 

15.  A  farm  rents  for  $500  a  year,  which  is  6J  per 
cent,  on  the  purchase  money,  at  $40  per  acre ;  how 
many  acres  in  the  farm  ? 

16.  Mr.  Jones  paid  $44  interest  on  a  note  running 
4  years  4  months  and  24  days,  at  5  per  cent. ;  what 
was  the  face  of  the  note  ? 

17.  A's  note  of  8200  was  given  for  a  carriage  ;  5 
years  7  months  and  6  days  afterwards,  $256  was 
given  for  the  note  ;  what  rito  p^^r  cent,  was  paid  ? 

18.  A  note  of  $300  on  interest  at  6  per  cent,  was 
given  for  a  span  of  horses  ;  when  the  note  was  taken 
up,  $330  was  paid  for  it ;  how  long  did  it  run  ? 

19.  B,  on  being  asked  how  much  he  owed  for  his 
farm,  replied,  "  I  pay  9  per  cent,  on  the  debt ;  if  I 
paid  but  7  per  cent.,  it  would  be  $60  in  my  favor 
yearly."     What  did  he  owe  ? 

20.  If  Aaron  had  purchased  his  horses  for  5  per 
cent,  less  than  he  did,  they  would  have  cost  him  $190 ; 
how  much  did  he  pay  for  them  ? 

21.  If  I  had  purchased  my  farm  for  6  per  cent, 
less  than  I  paid  for  it,  it  would  have  made  a  differ- 
ence in  the  purchase  money  of  $120 ;  what  did  the 
farm  cost  me  ? 

22.  A  speculator  sold  wheat  for  90  cents  a  bushel, 
and  in  so  doing  lost  10  per  cent. ;  what  should  he 
have  sold  it  for,  to  have  gained  15  per  cent.  ? 

23.  A  nurseryman  sold  apple   trees  at  $15   per 


144  INTELLECTUAL   ARITHMETIC.  [06, 

thousand,  and  cleared  |  of  Ms  receipts ;   what  per 
cent,  profit  did  he  make  ? 

24.  B  pays  ^400  a  year  for  the  use  of  100  acres 
of  land,  giving  8  per  cent,  of  its  value ;  what  is  it 
worth  per  acre  ? 

25.  I  bought  a  stock  of  goods  for  $800,  and  paid 
•$15  for  store  rent,  $8d  for  clerk  hire,  and  sold  them 
at  the  end  of  6  months ;  wliat  per  cent,  must  be 
made  on  the  goods  to  cover  expenses  ? 

26.  In  how  maiiy  years  will  a  man,  paying  inter- 
est at  7  per  cent,  on  a  debt  for  land,  pay  the  amount 
of  the  debt  in  interest  ? 

27.  A.  bought  a  farm  for  13000  ;  he  reahzed  $700 
from  the  sale  of  wheat,  $200  from  corn  and  barley, 
and  $100  from  fruit,  and  then  sold  the  farm  at  a  dis- 
count of  25  per  cent. ;  did  he  gain  or  lose,  and  how 
much  ? 

28.  B  bought  a  horse  for  $60,  then  sold  him  for 
$100,  and  repurchased  him  for  $80 ;  what  was  the 
gain  per  cent,  on  the  c.ri;??r^'J  inve^Lment  ? 

29.  A  milkman  sold  milk  for  4  cents  a  quart,  by 
which  he  cleared  ^  c£  the  i  ccei(.'te ;  b\t  milk  becoming, 
scarce,  he  sold  for  5  cents ;  what  per  cent,  did  he 
make  at  the  latter  price  ? 

SO.  A  walked  5  per  cent,  of  a  journey  of  300 
miles ;  20  per  cent,  of  the  remainder  he  rode  in  the 
stage,  and  the  rest  of  the  way  in  the  cars ;  how  far 
did  he  ride  in  the  cars  ? 

31.  A  mechanic  sold  a  buggy  for  $54,  and  gained 
20  per  cent.  ;  he  then  sold  another  for  $54,  and  lost 
10  per  cent. ;  did  he  gain  or  lose,  and  how  much  ? 

82.  A  dealer  sold  a  melodeon  for  $190,  and  lost 
5  per  cent,  on  it ;  he  then  sold  another  for  the  same 
money,  but  made  enough  to  balance  the  loss  on  tho 
first ;  what  per  cent,  did  he  make  on  the  second  ? 


97.]  INTELLECTUAL   ARITHMETIC.  145 

CHAPTER  IX. 

MISCELLANEOUS     EXAMPLES. 

97.  1.  A  gentleman,  owning  |  of  a  vessel,  sold 
I  of  his  share ;  what  part  of  the  vessel  does  he  still 
own  ? 

Analysis.  Since  he  sold  |  of  his  share,  he  would  have  i 
left,  and  ^  of  ^  is  ^.      Therefore,  ^c, 

2.  A  man,  owning  ^  of  a  share  in  the  Central  Rail- 
road, sold  I  of  it ;  what  part  of  a  share  has  he  left  ? 

3.  A  man,  having  |^  of  a  barrel  of  flour,  gave  \ 
of  it  to  a  poor  neighbor ;  what  part  of  a  barrel  has 
he  left  ? 

4.  Harry,  having  |  of  a  dollar,  gave  |-  of  it  for  a 
knife  ;  what  part  of  a  dollar  has  he  left  ? 

5.  A  man  sold  a  watch  for  818,  which  was  |  of 
what  it  cost  him  ;  how  much  did  he  lose  ? 

6.  A  grocer  sold  a  quantity  of  cheese  for  $45, 
which  was  |  of  what  it  cost  him ;  how  much  did  he 
gain  ? 

7.  A  threshing  machine  was  sold  for  1120,  at  a 
sacrifice  of  |  of  the  cost ;  what  was  the  loss  on  it  ? 

8.  Henry  having  lost  |  of  his  money  playing  cards, 
lent  \  of  the  remainder,  when  he  found  he  had  822 
left ;  how  much  had  he  at  first  ? 

9.  A  horse  was  sold  for  880,  which  was  |-  of  |  of 
twice  the  cost ;  what  was  lost  on  the  horse  ? 

10.  A  man  bought  a  wagon  for  854,  which  was  |- 
of  twice  as  much  as  he  sold  it  for  ;  what  did  he  gain  ? 

11.  Homer  had  15  marbles,  which  was  |  of  3 
times  as  many  as  Henry  had  ;  how  many  had  Henry  ? 

12.  Thomas  gave  4  cents  for  a  top,  which  was  f 
times  ^  of  what  money  he  had  ;  how  many  marbles, 
at  2  for  a  cent,  could  he  buy  with  what  he  had  left  ? 

10 


146  INTELLECTUAL   ARITHMETIC.  [97. 

13.  A  farmer,  after  selling  |  of  his  flock  of  sheep, 
had  20  left ;  how  many  had  he  at  first  ? 

14.  A  pole  was  standing  |  of  its  length  in  the  air, 
1^  of  the  remainder  in  the  water,  and  3  feet  in  the 
mud  ;  how  many  feet  in  the  air  ? 

15.  If  from  my  age  you  take  J  and  |  of  my  age,^ 
the  remainder  will  be  4  years  ;  how  old  am  I  ? 

16.  If  to  I  of  the  cost  of  A's  coat  you  add  $12 
the  sum  will  be  $20 ;  what  was  the  cost  of  the  coat  ? 

17.  A  drover,  being  asked  how  many  sheep  he 
had,  replied,  "  If  to  |-  my  number  you  add  80  sheep, 
the  sum  will  be  5  more  than  3  times  my  number ;  '^ 
how  many  had  he  ? 

18.  John  and  James  play  at  marbles  ;  John  wins 
16,  which  is  |  of  twice  as  many  as  James  now  has  ; 
when  they  began,  |  of  John's  equaled  |-  of  James's  ; 
how  many  had  each  when  they  began  ? 

19.  1^  of  Herbert's  age,  increased  by  10  years, 
equals  1^  times  his  age  ;  how  old  is  he  ? 

20.  A  cow  cost  $40  ;  |  of  this  sum  was  -^j  of  2| 
times  ^  of  the  cost  of  a  horse  ;  what  was  tlie  cost  of 
the  horse  ? 

21.  A.  was  25  years  of  age  when  he  was  married, 
and  his  age  was  |-  times  |  of  his  wife's  age  ;  how  old 
was  she  ? 

22.  A  post-office  Avas  robbed  by  a  clerk,  who  took 
I  of  the  money  in  the  drawer  ;  when  he  was  arrested, 
he  had  made  away  with  |  of  it,  and  had  $10  left ; 
how  much  was  in  the  drawer  at  first  ? 

23.  A's  farm  cost  $1500  ;  |  of  this  is  |  of  4  time& 
the  cost  of  the  barn  ;  wliat  did  the  barn  cost  ? 

24.  At  the  battle  of  Long  Island,  the  Americans 
lost  500  men  ;  |  of  this  number  was  |  of  --^^Q  of  their 
force  ;  how  many  men  had  they  in  the  field  ? 

25.  At  Ridgefield,  100  Americans  were  killed  ;  | 
of  the  slain  was  7-|-  times  j^-^  of  the  men  on  duty  ; 
how  many  on  duty  ? 


98.]  INTELLECTUAL   ARITHMETIC.  14T 

26.  The  American  loss  at  the  battle  of  Trenton, 
m  killed,  frozen,  and  wounded,  was  60  men  ;  ^  of 
this  number  was  2^-  times  yI-q  ^^  ^^^^  number  en- 
gaged ;  how  many  men  in  the  engagement  ? 

27.  At  the  assault  on  Quebec,  the  Americans  had 
100  killed  ;  |  of  this  number  was  If  times  ^V  of  the 
men  sent,  and  6  more  ;  how  many  men  in  the  de- 
tachment ? 

28.  The  American  loss  in  the  battle  of  Port  Royal 
Island  was  80  men  ;  2^  times  this  number  was  8-i- 
times  yV  of  the  number  in  the  field  ;  how  many  in 
the  field  ? 

29.  At  Germantown,  the  American  loss,  in  slain, 
wounded,  and  prisoners,  was  1200  ;  |-  of  this  num- 
ber was  8-1-  times  yoo  of  i  of  the  army,  lacking  1000 
men  ;  how  many  in  the  army  ? 


98.  1.  Divide  28  into  two  numbers  that  shall 
be  to  each  other  as  5  to  2. 

Analysis.  Since  the  nnmhers  are  to  each  other  as  5  to 
2,  the  given  sum  must  be  divided  into  7  equal  parts,  and  5  of 
those  parts  will  equal  one  of  the  mmibers,  and  2  of  them  the 

ither ;  the  numbers  will  be  ^  of  28  and  S  of  28,  equal  to  20 

wtd  8.      Therefore,  Sfc. 

2.  Two  men  bought  40  bushels  of  potatoes  ;  one 
paid  $6,  and  the  other  -$4  ;  how  many  bushels  should 
each  have  ? 

3.  Two  travelers,  49  miles  apart,  approach  each 
other ;  one  traA'cls  4  miles  an  hour,  the  other  3  miles 
an  hour  ;  how  many  miles  will  each  travel  ? 

4.  A  and  B  hired  a  horse  and  buggy  for  ^25  ;  A 
used  it  3  weeks,  B  2  weeks  ;  Avhat  should  each  pay  ? 

5.  Two  men  hired  a  pasture  for  f  24  ;  one  put  in 
5  cows,  the  other  put  in  3  cows  ;  what  should  each 
pay? 


148  INTELLECTUAL    AEITHMETIC.  [98, 

6.  Two  men  hired  a  field  for  $12  ;  one  put  in  2 
horses  for  2  weekSj  the  other  two  horses  for  4  weeks ; 
what  shoukl  each  pay  ? 

7.  John  had  9  cents,  and  Jay  had  7 ;  they  gave 
them  all  for  32  figs  ;  how  many  should  each  of  them 
liave  ? 

8.  A  and  B  enter  into  partnership ;  A  invests  §10 
for  5  months,  B  invests  ^5  for  8  months ;  they  gain 
$15  ;  what  is  each  man's  share  of  the  gain  ? 

9.  A,  B,  and  C  bought  a  horse ;  A  paid  $5  as 
often  as  B  $1  and  C  $3 ;  tliey  gained  $21  in  selling 
him  ;  wliat  is  each  man's  share  of  the  gain  ? 

10.  Taree  men  agree  to  mow  a  field  for  $10 ;  A 
sends  2  men  three  days,  B  sends  3  men  three  days, 
C  sends  2  men  two  and  a  half  days ;  what  shoukl 
each  receive  ? 

11.  A,  B,  and  C  traded  in  company ;  A  put  in 
$30,  B  $50,  and  C  such  a  sum  that  he  took  $10  of 
the  $12  gained  during  the  year;  what  was  the  gain 
of  A  and  B,  and  what  C's  stock  ? 

12.  An  ignorant  partner,  who  furnished  $500  of  a 
capital  ot*  $800,  on  which  $240  had  been  gained, 
took  $145  for  his  share  of  the  profits ;  did  he  gain 
or  lo33,  and  how  much  ? 

13.  Two  men  paid  $11  for  the  use  of  a  pasture; 
the  first  put  in  5  calves,  the  second  4  colts ;  what 
shoiild  each  pay,  provided  2  colts  consume  as  much 
as  3  calves  ? 

14.  A,  B,  and  C  hire  a  field  for  $42 ;  A  puts  in  5 
cows,  B  3  cows,  and  C  pays  |  of  the  rent ;  how  much 
must  A  and  B  pay,  and  how  many  cows  docs  C 
put  in  ? 

15.  Three  men  paid  $56  for  a  pasture ;  the  first 
put  in  9  oxen,  the  second  8  cows,  and  the  third  10 
calves ;  what  should  each  pay,  if  4  cows  eat  as  much 
as  3  oxen,  and  5  calves  as  much  as  4  cows  ? 


99.]  nsTELLECTUAL    AEITHMETIC.  149 

16.  Mary  and  Melissa  wrote  60  lines  in  a  copy 
book ;  Mary  wrote  i  as  many  lines  as  Melissa ;  liow 
many  lines  did  eacli  y\'rite  ? 

17.  A  gardener  gave  24:  pears  to  some  scliool 
children,  giving  each  girl  4  pears,  and  each  boy  3; 
the  boys  received  as  many  pears  as  the  girls ;  how 
many  children  were  there  'i 

18.  A  flither  divided  -$96  among  his  two  sons  and 
8  daughters,  giving  each  son  ^  as  much  as  each 
dauo-hter  ;  how  much  did  each  receive  ? 


99.  1.  Three  boys  have  76 marbles:  the  second 
has  2  more  than  the  first,  and  the  third  has  6  more 
than  the  second  ;  how  many  has  eacli  ? 

2.  James,  Henry,  and  Joseph,  together,  have  72 
apples ;  Henry  iias  2  more  than  James,  and  Joseph 
2  more  than  Henry ;  if  each  had  no  more  than 
James,  how  many  would  all  have  ? 

3.  If  each  had  as  many  as  Joseph,  h.ow  many 
would  all  have  ? 

4.  How  many  must  Joseph  give  James  tha^t  each 
may  have  the  same  number  ?     How  many  lias  each  ? 

5.  A,  B,  and  C  built  a  warehouse  for  $300 ;  B 
paid  8100  more  than  A,  and  C  paid  as  much  as  A 
and  B  ;  how  much  did  each  pay  ? 

6.  William  bought  a  ride,  a  watcli,  and  a  drum, 
for  $4:2  ;  for  the  rifle  he  gave  twice  as  much  as  for 
the  drum,  and  for  the  watch  twice  as  much  as  for 
the  rifle  ;  what  did  he  give  for  each  ? 

7.  A  span  of  horses,  wagon,  and  harness  cost 
$225 ;  the  difference  between  the  cost  of  the  horses 
and  wagon  was  1^  times  the  cost  of  the  liarness, 
and  the  cost  of  the  horses  was  4  times  tlie  cost  of  the 
harness  ;  what  was  the  cost  of  each  ? 

8.  B  traveled  114  miles  in  3  days ;  the  first  day 


150  INTELLECTUAL   ARITHMETIC.  [99. 

he  traveled  J  as  far  as  on  the  last  2  days,  and  the  last 
day  I'  as  far  as  on  the  first  two  days  ;  how  far  did  he 
travel  each  day  ? 

9.  A  laborer  in  one  week  dug  5  rods  more  than 
-J  the  length  of  a  ditch,  and  the  next  week  he  dug  the 
remaining  20  rods  ;  how  long  was  the  ditch  ? 

Analysis.  Since  he  dug  5  rods  more  than  ^  of  the 
ditch  the  first  week,  the  remainder,  20  rods,  increased  by  5 
rods,  must  equal  ^  the  ditch  ;  20  rods  +  5  rods  =  25  rodsy 
which  is  i  of  twice  25,  or  50  rods.      Therefore,  S^c, 

10.  A  farmer,  owing  a  store  debt,  paid  at  one 
time  $10  more  than  -^  of  it,  at  another  $20  more 
than  i  of  the  remainder,  and  gave  a  note  of  |20  for 
the  balance  of  the  debt ;  what  was  the  amount  of 
the  debt  ? 

11.  Arthur  gave  2  more  than  -|  of  his  pennies  for 
a  top,  1  more  than  |  of  the  remainder  for  a  wliip, 
and  had  4  left ;  how  many  pennies  had  he  at  first  ? 

12.  A  grocer,  selling  beer,  drew  ^  a  gallon  more 
than  l  the  contents  of  a  keg  one  day,  the  next  day 
he  drew  J  a  gallon  more  than  -|  of  the  remainder, 
and  the  third  day,  when  he  went  to  draw,  he  found  the 
keg  was  empty ;  how  many  gallons  in  the  keg  at  first  ? 

13.  A  and  B  have  $55  ;  -I-  of  A's  money  equals  -| 
of  B's  ;  how  many  dollars  has  each  ? 

Analysts.  Since  ^  of  A's  money  equals  f  of  B's,  2 
halves,  or  all  of  A's,  ivill  equal  2  times  f ,  or  f  of  B's  ;  then 
A  has  6,  and  B  5  equal  parts  of  the  money,  and  both  have 
11  parts  ;  -^\  of  $55  is  $5,  or  "l  part ;  G  times  $5  are  $30, 
or  A's  share  ;  and  5  times  $5  are  $25,  or  B's  share.  TJiere- 
fore,  ^c. 

14.  If  34  apples  he  divided  between  John  and 
Mary,  so  that  |  of  John's  may  equal  |  of  Mary's, 
how  many  will  each  have  ? 


.]  INTPXLECTUAL   ARITHMETIC.  151 

15.  A  and  B  have  together  83  sheep ;  f  of  A's 
flock,  increased  by  8  sheep,  is  equal  to  B's  flock  ;  how 
many  sheep  has   each  ? 

16.  If  10  cents  be  taken  from  4  of  Mary's  money, 
the  remainder  will  be  equal  to  Susan's  ;  the  girls, 
together,  have  39  cents ;  how  many  cents  has  eacli  ? 

17.  Homer  has  3  marbles  more  tlian  Silas,  and  ^ 
of  Homer's  marbles  equal  |  of  Silas's ;  how  mani" 
has  each  ? 


100.  1.  One  man  will  drink  a  gallon  of  beer  in  3 
days  ;  another  will  drink  a  gallon  in  4  days  ;  how  long 
will  a  gallon  last  both  of  them  ? 

2.  Julia  can  do  the  washing  in  7  hours  ;  with 
Jane's  assistance  she  can  do  it  in  1  hours  ;  in  what 
time  can  Jane  do  it  ? 

3.  Two  boys  can  pitch  a  quantity  of  hay  in  5 
hours ;  the  first  can  do  it  in  9  hours  ;  in  what  time 
can  the  second  do  it  ? 

4.  A  cistern  can  be  emptied  by  2  pipes  in  3| 
hours,  but  1  pipe  will  empty  it  in  7^  hours  ;  in  how 
many  hours  will  the  other  empty  it  V 

5.  A  can  make  a  vest  in  |  of  a  day,  B  in  |,  and  C 
in  I  of  a  day  ;  hoAV  many  more  vests  can  A  and  B 
make  in  a  day  than  C  can  ? 

6.  Susan  can  knit  a  pair  of  mittens  in  |  of  a 
day,  and  Sarah  can  knit  a  pair  in  |  of  a  day  ;  how 
many  pairs  can  both  knit  in  a  day  ? 

7.  What  part  of  a  day  must  Sarah  assist  Susan 
that  Susan  may  complete  2  pairs  ? 

8.  What  part  of  a  day  must  Susan  assist  Sarah 
that  Sarah  may  complete  3  pairs  ? 

9.  Jason  can  hoe  10  rows  of  corn  in  |  of  an 
hour,  and  Jesse  can  hoe  them  in  |  of  an  hour ;  in 
what  time  can  both  together  hoe  them  ? 


152  INTELLECTUAL   ARITHMETIC. 

10.  In  what  time  can  Jason  hoe  what  remains 
after  Jesse  has  hoed  |-  an  hour  ? 

11.  In  what  time  can  Jesse  hoe  what  remains 
after  Jason  has  hoed  ^  of  an  hour  ? 

12.  How  many  rows  can  both  hoe  in  1  hour  ? 

13.  A  and  B  can  clear  a  field  in  15  days ;  with 
the  help  of  C  they  can  do  it  in  9  days  ;  in  how  many 
days  can  C  do  it  ? 

14.  A  and  B  can  dig  a  well  in  6  days,  A  and  C  in 
8  days,  and  B  and  C  in  9  days ;  in  how  many  days 
can  each  dig  it,  working  alone  ? 

15.  In  how  many  days  can  they  do  it  working 
together  ? 

16.  Patrick,  Peter,  and  Pliilo  can  dig  40  rods  of 
ditch  in  10  days ;  Patrick  and  Peter  can  do  it  in  15 
days  ;  Peter  and  Philo  can  do  it  in  lo^  days  ;  in  how 
many  days  can  Patrick  and  Philo  dig  28  rods  ? 

17.  How  long  will  it  take  each  man  to  dig  30  rods  ? 

18.  Henry  and  Harlan  can  cut  a  field  of  corn  in 
6|  days ;  Harlan's  day's  work  exceeds  Henry's  by  I 
oi*  Henry's  ;  in  how  many  days  can  each  cut  the  field  ? 

19.  Three  men  can  do  a  piece  of  work  in  10  days  ; 
the  first  does  |  as  much  as  the  second,  the  third  does 
-|  as  much  as  the  first  and  second;  in  how  many 
days  will  each  do  it  ? 

20.  In  how  many  days  will  the  first  and  second 
doit? 

21.  In  how  many  days  will  the  first  and  third  do  it  ? 

22.  In  how  many  days  will  the  second  and  third 
doit? 

23.  A,  B,  and  C  can  do  a  piece  of  work  in  8  days  ; 
B  and  C  can  do  it  in  12  days,  and  A  and  B  in  10 
days ;  in  how  many  days  can  each,  working  separately, 
doit? 

24.  A  cistern  can  be  discharged  by  3  pipes  in  4 
hours ;  the  first  and  second  pipes  will  discharge  it  in 


101.]  INTELLECTUAL   ARITHMETIC.  153 

8  hours  ;  the  first  and  third  in  6  hours  ;  in  what  time 
will  each  pipe  discharge  it  ? 

25.  Three  men  can  trench  a  field  in  10  days ;  A 
and  B  can  do  it  in  20  days  ;  B  and  C  can  do  it  in  15 
days ;  in  how  many  days  can  A  and  C  trench  the 
same  field  ? 

26.  A  barrel  of  flour  would  last  a  brother,  sister, 
and  servant  30  days ;  when  tlie  brother  Avas  absent 
it  would  last  60  days  ;  when  the  sister  was  absent  it 
would  last  45  days  ;  how  long  would  it  last  the  sistei" 
after  all  had  iised  from  it  20  days  ? 


101.  1.  Benjamin,  meeting  some  beggars,  gave 
each  of  them  5  cents ;  had  he  given  them  7  cents 
apiece,  ir  would  have  taken  8  cents  more  ;  how  many 
beggars  were  there  ? 

Analysis.  Since  2  cents  was  the  increase  paid  to  1 
beggar^  and  8  cents  the  increase  paid  to  all,  there  were  as 
many  beggars  as  2  is  contained  times  in  8,  which  is  4  times, 
llierefore,  S^c. 

2.  Edward  gave  6  plums  to  each  of  his  playmates, 
and  had  9  remaining ;  had  he  given  each  of  them  8, 
he  would  have  had  but  1  left ;  how  many  playmatecs 
had  he  ? 

3.  Three  times  a  certain  number  is  15  less  than  6 
times  the  same  numl^icr  ?  what  is  tlie  number  ? 

4.  SiTsan,  purchasing  calico,  found  that  if  she 
took  that  at  8  cents  a  yard  she  would  liavc  11  cents 
left ;  ]nit  if  she  took  that  at  12  cents  a  yard  she 
would  need  17  cents  to  pay  for  it ;  how  many  yards 
did  she  want  ? 

5.  4  times  a  number  is  15  less  than  6|-  times  the 
same  number  ;  what  is  tlie  number  ? 

6.  John,  being  asked  how  many  marbles  he  had, 
replied,  "  f  of  them  exceed  J  of  them  by  4."  How 
many  had  he  ? 


154  INTELLECTUAL   ARITHMETIC.  [101. 

7.  5^-  times  a  number  is  21  greater  than  3|  times 
the  same  number  ;  what  is  the  number  ? 

8.  If  24  chestnuts  be  divided  among  some  boys, 
giving  4  apiece  to  -|-  of  them,  and  2  apiece  to  the 
others,  how  many  boys  are  there  ? 

Analysis.  Smce  one  hoy  received  4  chestnuts  as  often 
as  another  received  2  chestnuts^  2  hoys  received  6  chestnuts; 
there  were  as  many  times  2  hoys  as  6  is  contained  times 
in  24,  which  is  4  times,  and  4  times  2  hoys  are  8  hoys» 
Therefore,  ^c, 

9.  Mary  gave  her  chickens  26  grains  of  corn ;  J 
of  them  had  5  grains  each,  the  others  but  3  each; 
how  many  chickens  had  she  ? 

Note.    The  above  gives  the  following  question  :  — 

10.  5  times  |-  of  a  certain  number,  phis  3  times  -J 
of  the  same  number,  is  26  ;  what  is  the  number  ? 

11.  A  class  received  29  merit  marks ;  -J  of  them 
received  5  apiece,  -|  of  the  remainder  3  apiece,  |-  of 
the  remainder  2  apiece,  and  the  rest  1  apiece ;  how 
many  scholars  in  the  class  ? 

12.  26  melons  were  stolen,  |  of  the  party  getting 
4  each,  the  rest  3  apiece,  except  2,  who  obtained  but 
2  apiece  ;  how  many  were  there  in  the  party  ? 

Analysts.  Had  the  last  2  ohtained  3  each,  there  would 
have  been  28  melons  ;  then  4  times  ^  of  a  number,  plus  3 
times  ^  of  the  some  number,  or  ^,  woidd  equal  28.  Since 
28  is  J  of  a  number,  J-  of  28,  or  4,  is  ^,  and  4  is  ^  of  2 
times  4,  or  8.      Therefore,  S^c. 

13.  4  times  ^  of  a  number,  plus  3-|-  times  the 
same  number,  is  equal  to  28  plus  5  ;  what  is  the 
number  ? 

14.  Henry  said  that  4  years  more  than  J  of  his 
age,  increased  by  5  times  ^  of  it,  and  that  sum  by  4 
times  \  of  his  age  less  4,  would  make  the  siuii  50 
years ;  how  old  was  he  ? 


1®!.]  INTELLECTUAL   ARITHMETIC.  *        155 

15.  A  drover  paid  $5  a  head  for  -J  of  his  flock,  $4 
a  head  for  as  many  more,  -fo  a  head  for  -|  of  the 
remainder,  and  ^2  a  head  for  the  rest ;  the  flock  cost 
$115  ;  how  many  sheep  had  he  ? 

16.  A  grocer  received  -flO  for  a  lot  of  baskets  ; 
for  ^  of  them  he  had  6  dimes  each,  for  ^-  of  the  re- 
mainder plus  3,  4  dimes  each,  for  -J  of  the  rest  plus 
2,  3  dimes  each,  and  for  the  rest  2  dimes  each ;  lidKv 
many  baskets  did  he  sell  ? 

17.  5  times  Henry's  age  is  3  more  than  4  times  ^ 
of  it  increased  by  6  times    ~  of  it ;  how  old  is  he  ? 

Analysis.  5  ti77ies  Henrxfs  age  equals  ^^-^  4  times  §  of 
it^  plus  6  ti?7ies  ^  of  it,  equals  -'5*-,  a7id  ^-^  less  ^-^-  equals  ^ 
of  it,  which,  according  to  the  conditions  of  the  question,  is 
3  ;  and  3  is  -^  of  3  times  3,  or  9.      Therefore,  ^t. 

18.  6  times  a  number  is  4  less  than  7  times  |  of 
it,  plus  5  times  \  of  the  same  number ;  what  is  the 
iiumber  ? 

19.  Bridget,  wishing  to  get  a  certain  number  of 
pounds  of  meat,  found,  if  she  took  beef  at  5  cents, 
slie  would  have  4  cents  left ;  if  pork  at  7  cents,  she 
had  not  money  enough  to  pay  for  it ;  and  therefore 
she  took  |-  of  the  quantity  in  beef,  the  rest  in  pork, 
and  paid  for  it ;  how  many  pounds  did  she  get  ? 

20.  Four  times  a  number  is  6  greater  than  5  times 
|-  of  the  same  number  ;  what  is  the  number  ? 

21.  A  farmer,  wishing  to  buy  a  flock  of  sheep, 
found,  if  he  paid  $2  a  head,  he  would  have  $80  left ; 
if  he  paid  ^h  a  head,  he  had  not  enough  to  pay  for 
them  ;  if  he  took  |-  the  number  at  each  price,  he 
could  just  pay  for  them  ;  how  many  sheep  would 
his  money  buy  ? 

22.  Twice  f  of  a  number  equals  the  number  plus 
8  ;  what  is  the  number  ? 


156  INTELLECTUAL   ARITHMETIC. 


I® 2!.  1.  The  sum  of  two  numbers  is  27 ;  their 
difterence  5  ;  what  are  the  numbers  ? 

Analysis.  Since  27  is  the  sum  of  two  numbers  v:hose 
difference  is  5,  27  less  5,  or  22,  would  be  twice  the  less  num- 
ber ;  ^  of  22  is  11,  the  less  number,  which  increased  by  0 
equals  IG,  or  the  greater  number.      Therefore,  S^c. 

2.  James  and  John  together  have  19  peaches  ; 
John  has  3  more  than  James  ;  how  many  lias  each  ? 

3.  Hobart  has  9  marbles  more  than  Herbert,  and 
together  they  have  31  ;  how  many  has  each  ? 

4.  Two  men  are  37|  miles  apart,  and  trayel 
toward  each  other  ;  when  they  meet,  one  has  trav- 
eled 5|-  miles  more  than  the  other  ;  how  far  has 
each  traveled  ? 

5.  Horace,  finding  he  had  5  more  apples  than 
Homer,  gave  him  3,  when  they  together  had  21 ; 
how  many  had  each  then  ? 

6.  Mary  has  twice  as  many  berries  as  Martha,  and 
together  they  have  12  quarts  ;  how  many  quarts  has 
each  ? 

7.  A  farmer  had  47  sheep  in  two  fields  ;  in  one 
field  there  were  5  more  than  twice  as  many  as  in  the 
other  ;  how  many  were  there  in  each  field  ? 

8.  There  are  54  bushels  of  corn  in  two  bins  ;  in 
one  bin  there  are  6  bushels  less  than  half  as  many  as 
there  are  in  the  other ;  how  many  bushels  in  each  ? 

9.  A  man  bought  a  watch"  and  chain  for  $96  ;  the 
watch  cost  $4  less  than  3  times  the  cost  of  the  chain  ; 
what  was  the  cost  of  each  ? 

10.  Hiram  and  Harvey  built  wall  11  days  ;  Hiram 
received  2  dimes  a  day  more  than  Harvey,  and  they 
both  received  $25.30  ;  what  did  each  receive,  and 
how  much  per  day  ? 

11.  The  sum  of  A's  and  B's  ac-cs  is  60  years  ;  6 
years  ago,  A's  age  was  ^  of  B's  ;  what  are  their  ages 
now  ? 


II O^.]  INTELLECTUAL   ARITHMETIC.  157 

12.  A  horse  and  cow  cost  $124 ;  the  horse  cost 
'$4  more  than  3  times  the  cost  of  the  cow ;  what  was 
the  cost  of  each  ? 

13.  A  farmer  paid  $24  for  a  colt  and  cow ;  |  the 
cost  of  the  colt,  multiplied  by  j  the  cost  of  the  cow, 
equaled  the  cost  of  the  cow ;  what  did  he  pay  for 
each  ? 

^  14.  A  lady  purchased  a  dish  and  cover  for  24 
dimes;  -J  of  the  cost  of  the  dish,  increased  by  the 
difference  between  the  cost  of  the  dish  and  cover, 
equals  the  cost  of  the  cover  ;  what  was  the  cost  of 
each  ? 

15.  A  grocer  purchased  25  pounds  of  butter  of 
two  women  ;  |-  of  the  number  of  pounds  he  took  of 
one,  increased  by  the  difference  between  tlio  amounts 
purchased  of  both,  equals  the  number  of  pounds  he 
took  of  the  other  ;  how  many  pounds  did  each  sell  ? 

16.  The  sum  of  two  numbers  is  10  ;  their  differ- 
ence is  equal  to  J  of  the  greater  number  ;  what  are 
the  numbers  ? 

17.  A  Avagon  cost  838  ;  -^j  of  the  cost  of  the  wood 
work  exceeds  the  cost  of  ironing  it  by  ^  of  the  dif- 
ference between  the  expense  of  the  two ;  what  was 
the  cost  of  each  ? 

18.  Emily  purchased  some  lace  and  some  ribbon 
for  30  cents  ;  l-  the  cost  of  the  lace,  increased  by  -i- 
the  difference  between  the  cost  of  the  lace  and  rib"- 
bon,  equals  the  cost  of  the  ribbon ;  what  did  she  pay 
for  each  ? 

19.  Wilber  paid  20  shillings  for  a  pair  of  skates  ' 
and  a  knife  ;  twice  the  difference  between  the  cost  of 
the  two,  plus  J  the  cost  of  the  knife,  equals  the  cost 
of  the  skates  ;  what  did  he  pay  for  each  ? 

20. ,  A  horse  and  harness  cost  $34  ;  |-  of  the  cost 
of  tlie  horse  is  $1  more  than  the  cost  of  the  harness  ; 
what  was  the  cost  of  each  ? 


158  INTELLECTUAL   ARITHMETIC.  [ 


1.  A  grocer  paid  112.60  for  30  bushels  of 
potatoes,  giving  50  cents  a  bushel  for  good  ones,  and 
20  cents  a  bushel  for  poor  ones ;  how  many  bushels 
were  good  ? 

Analysis.  If  all  had  heen  good,  he  woidd  have  paid 
$15,  or  $2.40  more  than  he  did;  each  bushel  of  poor  ones 
made  a  difference  of  30  cents;  hence  there  were  as  many 
bushels  of  poor  ones  as  30  cents  (the  difference  on  1  bushel) 
is  contained  times  in  $2.40,  {the  difference  on  all,)  which  is 
8  times,  equal  to  8  bushels  of  poor  ones  ;  the  difference  be- 
tween 30  bushels  and  8  bushels  is  22  bushels,  equal  to  the 
good  ones.      Therefore^  ^c. 

2.  A  farmer  bought  28  sheep  for  $76,  paying  |3 
for  old  sheep,  and  $2  for  yearlings ;  how  many  old 
sheep  ? 

3.  A  flour  merchant  paid  $82  for  20  barrels 
of  flour,  giving  $4.50  for  first  quality,  and  $3.50 
for  second  quality ;  how  many  barrels  were  first 
quality  ? 

4.  Henry  sold  his  watch  for  $18,  and  by  so  doing 
lost  I  of  what  it  cost ;  what  did  it  cost  ? 

5.  A  man,  employing  an  equal  number  of  men 
and  boys,  paid  each  boy  5  dimes,  and  each  man  7 
dimes,  and  to  them  all  he  paid  $7.20 ;  how  many 
were  there  of  both  ? 

6.  An  old  lady  sold  an  equal  number  of  chickens 
and  turkeys  for  $4,  receiving  for  chickens  3  dimes 
each,  and  for  turkeys  5  dimes  each ;  how  many  fowls 
did  she  sell  ? 

7.  A  speculator  bought  an  equal  quantity  of 
wheat  and  berans,  giving  $1.50  per  bushel  for  wheat, 
and  $1  for  beans ;  the  wheat  cost  $7  more  than  the 
beans  ;  how  many  bushels  of  beans  did  he  buy  ? 

8.  A  man  engaged  to  Avork  25  days,  on  condition 
that  he  should  receive  $2  for  every  day's  labor,  and 


103.]  INTELLECTUAL   ARITHMETIC.  lo9 

pay  $1  for  board  every  day  lie  was  idle  ;  he  received 
at  settlement  ^38  ;  how  many  days  was  he  idle  V 

Analysis.  As  mcmy  days  as  $3,  (the  difference  made 
hy  1  idle  day^')  is  contained  times  in  $12,  {the  difference 
made  hy  all  the  idle  days,)  which  is  4  times,  llierefore  he 
was  idle  4  days. 

9.  A  man  was  engaged  for  20  days  to  copy,  re- 
ceiving $2.50  for  every  day's  labor,  and  forfeiting  $>1 
for  every  day  he  was  idle ;  he  received  $48 ;  how 
many  days  did  he  copy  ? 

10.  Job,  having  some  chestnuts,  gave  |  of  them 
to  John,  who,  after  eating  6,  gave  -|  of  what  remained 
to  his  sister,  and  still  had  5  left ;  how  many  had  Job  ? 

Analysis.  If  John  gave  f  to  his  sister,  the  5  left  was  {  ; 
5  is  ^  of  4:  times  5,  or  20,  a?id  20,  plus  the  Q  he  ate,  make 
26,  which  is  f  of  Job's,  ^c. 

11.  Mary  gave  |  of  her  flowers  to  her  playmates^ 
I  of  the  remainder  to  her  teacher,  and  had  2  left ; 
how  many  had  she  at  first  ? 

12.  A  farmer  sold  |  of  1\  times  his  flock,  and 
had  12  sheep  remaining ;  how  many  sheep  had  ha 
at  first  ? 

13.  A  man  paid  $5  more  than  f  of  his  grocer' et 
bill  ;  soon  after  he  paid  -|  of  what  remained  unpaid^ 
when  he  found  83  was  still  due  ;  what  was  the 
amount  of  his  bill  ? 

14.  John  paid  $10  more  than  J  of  his  year's 
waores  for  clothes,  $12  for  a  watch  ;  he  then  lent  1^ 
of  what  he  had  left,  and  having  paid  $3  for  a  pair  of 
boots,  had  $5  left ;  what  were  his  wages  ? 

15.  A  laborer  engaged  to  work  20  days,  on  con- 
dition that  he  should  have  12  dimes  for  a  day's  labor, 
and  pay  2  dimes  for  every  idle  day  for  board  ;  he 
received  as  many  dollars  as  he  worked  days ;  how 
many  days  was  he  idle  ? 


160  INTELLECTUAL  ARITHMETIC.  [fi©4, 

l®4.  1.  A  rope  28  feet  in  length  was  broken  so 
that  |-  of  the  longer  piece  was  equal  to  the  shorter ; 
what  was  the  length  of  each  piece  ? 

Analysis.  Tlie  longer  'piece  is  divided  into  5  equal 
parts,  2  of  which  equal  the  shorter ;  the  sum  of  the  2 
pieces  is  7  equal  parts,  one  of  which  equals  4-  of  2S  feet, 
or  4  feet ;  2  parts  equal  2  times  4  feet,  which  are  8  feet, 
the  shorter  piece  ;  5  parts  equal  5  times  A  feet,  which  are  20 
feet,  the  longer  piece.      2'hertfore,  Sfc. 

2.  A  tree  56  feet  high  was  broken  in  a  storm  ;  |  of 
the  part  standing  was  equal  to  the  part  broken  off; 
what  was  the  length  of  each  part  ? 

3.  Henry  and  Horace  have  45  marbles  ;  Horace 
has  I  as  many  as  Henry  ;  how  many  has  each  ? 

4.  A  grocer,  having  opened  a  barrel  containing 
160  pounds  of  sugar,  took  out  |  as  much  as  he  left ; 
how  many  pounds  were  left  in  the  barrel  ? 

5.  A  traveler  paid  Go  cents  for  his  supper  and 
lodging,  paying  |  as  much  for  his  supper  as  for  his 
lodging  ;  what  did  he  pay  for  his  supper  ? 

6.  A  horse  and  wagon  cost  $170  ;  the  liorse  cost 
11  times  as  much  as  the  wagon  ;  what  Avas  tiie  cost 
of  each  ? 

7.  Henry  traveled  140  miles  in  2  days  ;  the  first 
day  he  traveled  1 1  times  as  far  as  he  did  the  second  ; 
liow  far  did  he  travel  each  day  ? 

8.  From  BuffyJo  to  Bergeo  k  50  miles,  from  Bergen 
to  Utica  is  1|-  times  as  far  as  from  Utica  to  Schenec- 
tady, which  is  280  miles  from  Buffalo  ;  how  many 
miles  from  Buffalo  to  Utica  ? 

9.  David  caught  a  trout  17  inches  long ;  the  tail 
was  I  as  long  as  the  body,  and  the  head  was  3  inches 
long  ;  how  long  was  the  tail  ? 

10.  Divide  36  into  2  such  parts  that  1|  times 
one  shall  equal  the  other. 


104.]  INTELLECTUAL   ARITHMETIC.  161 

11.  Homer  and  Harlan  have  48  apples ;  -|  of 
Homer's,  plus  6,  equal  the  number  Harlan  has ; 
how  many  has  each  V 

Analysis.  Harlan  has  6  more  than  |-  as  many  as  Ho- 
mer, which  makes  the  sum  48,  6  greater  than  if  he  had  but 
^  as  many ;  Homer's  are  divided  into  4  parts,  of  ichich  3 
parts  plus  6  apples  are  equal  to  Harlan's ;  then  4  parts 
plus  3  parts,  plus  6  apples,  equal  48,  7  parts  equal  42, 
and  y  of  42,  or  6,  equals  1  part.  3  parts  plus  6  equal 
24,  the  number  Harlan  has,  and  4  parts  equal  24,  the  num- 
ber Homer  has.      Therefore,  S^c. 

12.  Rochester  is  52  miles  from  Geneva,  via  Vic- 
tor ;  -j^Y  of  the  distance  from  Geneva  to  Victor,  plus 
4  miles,  equals  the  distance  from  Victor  to  Rociies- 
ter  ;  how  far  is  Victor  from  each  place  ? 

18.  From  the  ground  to  the  top  of  a  church  steeple 
is  146  feet ;  |  of  the  height  of  the  steeple  above  the 
church,  plus  6  feet,  is  equal  to  the  heiglit  of  the  church ; 
wliat  is  the  height  of  the  steeple  above  the  church  ? 

14.  A  jar  and  cover  weigh  18  pounds ;  |-  of  the 
weight  of  the  cover,  increased  by  12  pounds,  equals 
the  weight  of  the  jar  ;  Avhat  is  the  weight  of  each  ? 

15.  A  coat  and  vest  cost  $19  ;  ^  of  the  cost  of  the 
coat,  plus  83,  equals  the  cost  of  the  vest ;  what  is  the 
cost  of  each  ? 

16.  Wilson  has  15  oranges  and  lemons ;  -J-  of  the 
oranges  equals  \  of  the  lemons ;  how  many  of  each 
has  he  ? 

Analysis.  Since  ^  of  the  oranges  equals  ^  of  the  lemons, 
f ,  or  all  the  oranges,  equcd  §  of  the  lemons ;  we  then  have 
the  oranges  and  lemons  divided  into  5  equal  parts,  2  parts 
of  which  equal  the  oranges,  and  3  tlie  lemons,  ^c. 

17.  A  father  gave  his  2  sons  50  cents ;  ^  of 
George's  money  was  equal  to  |  of  Abel's  ;  how  many 
cents  had  each  ? 

18.  Andrew  has  34  marbles ;  |  of  the  gray  ones 

11 


16^  INTELLECTUAL  ARITHMETIC.  [S04» 

equal  j-  of  the  black  ones  ;  how  many  of  each  kind 
were  there  ? 

19.  The  sum  of  two  numbers  is  62 ;  -|  of  one 
equal  |  of  the  other ;   what  are  the  numbers  ? 

20.  A  purse  and  contents  are  valued  at  46  shil- 
lings ;  I  of  the  value  of  the  purse  is  equal  to  |  of 
the  value  of  what  is  in  it ;  what  is  the  purse  worth  ? 

21.  A  person,  being  asked  the  time  of  day,  replied, 
*'  The  time  past  noon  is  equal  to  ^  of  the  time  to 
midnight."     What  was  the  hour  ? 

Analysis.  The  time  to  midnight  is  divided  into  5  equal 
parts,  one  of  which  equals  the  time  past  noon  ;  then  5  parts 
plus  1  part  equals  6  paints; and  12  hours,  the  time  from 
noon  to  midnight,  must  he  ^  of  the  time  it  lached  of  being 
Tnidnight ;  since  12  is  f,  \,  which  is  ^  o/*|,  ivill  be  ^  of  12 
hours,  which  is  2  hours.  Therefore  the  hour  was  2  o'clock, 
P.M. 

22.  What  was  the  time,  provided  |  of  the  time 
past  midnight  equaled  the  time  to  10  o'clock,  A.  M.  ? 

23.  f  of  the  time  from  this  instant  to  5  o'clock, 
P.  M.,  equals  ^  of  the  time  past  midnight;  what  is 
the  time  of  day  ? 

24.  Peter  said  to  John,  "  1|  times  my  age  is  If 
times  your  age,  and  the  sum  of  our  ages  is  36  years." 
What  was  the  age  of  each  ? 

25.  A  bin  whose  capacity  was  44  bushels  was 
partly  filled  with  grain  ;  2^  times  wliat  was  in  it  was 
2-|-  times  what  it  would  take  to  fill  it ;  how  many 
more  bushels  would  fill  it  ? 

26.  A  person,  inquiring  the  distance  to  Cincinnati, 
was  told  that  3|  times  what  it  lacked  of  being  88 
miles  was  1|  times  what  it  exceeded  39  miles  ;  how 
far  was  he  from  Cincinnati  ? 

27.  The  number  of  miles  that  the  distance  from 
Charleston  to  Columbia  exceeds  100  miles  equals  1^ 
times  the  distance  it  lacks  of  being  150  miles ;  how 
far  is  it  from  Charleston  to  Columbia  ? 


lOo.]  INTELLECTUAL   ARITHMETIC.  163 

lOo.  1.  Two  pieces  of  cloth  contain  88  yards ; 
I  of  the  first  piece  equals  |  of  the  second,  phis  4 
yards  ;  how  many  yards  in  each  piece  ? 

Analysis.  If  §  equal  f  -|-  4,  ^  will  equal  h  of  ^  -\-  4, 
which  is  4^  -j-  2,  this  is  -^  of  3  times  ^ -\- '1,  or  f  -["  ^  > 
then  we  have  1  piece  equal  to  ^  the  other  plus  6  yards^  or  1 
•piece  divided  into  5  parts,  and  3  of  these  parts  plus  6  yards 
equal  the  other  piece  ;  hence  5  parts  plus  3  parts  plus  6  yards 
equal  38  yards,  or  8  parts  and  6  yards,  equal  38  yards  ;  38 
yards  minus  6  yards  equal  32  yards,  or  8  parts,  S^-c. 

2.  A  lad  inquiring  his  mother's  age,  his  father 
replied,  "  |  of  my  age  is  9  years  more  than  |-  of 
your  mother's,  and  the  sum  of  our  ages  is  72  years." 
How  old  was  his  mother  ? 

3.  Two  men  built  38  rods  of  wall ;  |  of  what  one 
built,  plus  4  rods,  is  equal  to  |-  of  wdiat  the  other 
built ;  how  many  rods  did  each  build  ? 

4.  Hiram  and  Richard  sheared  67  sheep  ;  -^  of  the 
number  Hiram  sheared  was  4  more  tlian  |-  of  the 
number  Richard  sheared  ;  how  many  did  each  shear  ? 

5.  What  is  the  time,  providing  |  of  the  time  past 
midnight,  plus  1^^  hours,  equals  |  of  tlie  time  to 
midnight  ? 

6.  A,  being  asked  his  age,  replied,  "  1\  times  what 
I  lack  of  being  a  hundred  years  old  is  9  years  more 
than  1|-  times  what  my  age  exceeds  64."  What  was 
his  ao'e  ? 

7.  A  rope  was  cut  into  3  pieces ;  the  first  piece 
was  5  feet  long,  the  second  was  as  long  as  the  first 
plus  -|-  of  the  third,  and  the  third  was  as  long  as  the 
other  two ;  wiiat  was  the  length  of  the  rope  ? 

Analysis.  Since  the  third  piece  is  as  long  as  the  other 
two,  it  must  he  ^  of  the  rope  ;  the  second  piece,  being  J-  as 
long,  is  i;  and  the  o  feet  which  the  second  exceeds  J-,  with 
the  ^  feet  of  the  first  piece,  make  10  feet,  which  must  he  the 
other  fourth  ;  4  times  10  is  40.      Tlierefore,  S)C. 


164  INTELLECTUAL   ARITHMETIC.  [Mt^, 


8.  The  Lead  of  a  fish  is  7  inches  long,  the  tail  is 
as  long  as  the  head  and  |  of  the  body,  and  the  body 
is  as  long  as  the  head  and  tail ;  what  is  the  length  of 
the  fish  ? 

9.  A  piece  of  steel  was  broken  into  3  pieces;  the 
first  piece  was  |-  of  the  whole,  the  second  weighed  o 
pounds,  and  the  third  weighed  as  much  as  tlie  other 
two  ;  what  was  the  weight  of  the  whole  ? 

10.  Three  men  dig  potatoes  ;  the  first  digs  ^  of 
the  whole,  lacking  2  bushels,  the  second  digs  5  bush- 
els, and  the  third  digs  as  many  as  the  other  two ; 
how  many  bushels  did  all  dig  ? 

11.  From  Batavia  to  Avon  is  21  miles ;  this  dis- 
tance, plus  the  distance  from  Bath  to  Corning,  and 
12  miles  more,  equals  the  distance  from  Avon  to 
Bath  ;  from  Bath  to  Corning  is  |-  of  the  whole  dis- 
tance ;  how  far  from  Batavia  to  Corning  ? 

12.  A  farmer  took  money  for  stock,  as  follows : 
S18  for  swine,  $3  more  than  -J  of  the  whole  for  sheep, 
and  for  cattle  $1  less  than  |  as  much  as  for  sheep 
and  swine  ;  liow  many  dolia/s  did  he  receive  ? 

13.  A  third  and  ^  a  third  of  12  is  |  of  twice  wha^t 
number  ? 

14.  Stephen  spent  |  of  his  money,  and  afterward 
earned  f  as  much  as  he  had  spent,  when  he  bad  $16.50 
l2S3  than  at  first ;  how  much  had  he  at  first  ? 

15.  If  I  of  a  ton  of  hay  cost  |-  of  an  eagle,  how 
many  dollars  vfill  J  of  a  ton  cost  ? 

16.  A  is  6  years  more  than  -J  as  old  as  B,  C  is  §■ 
as  old  as  A,  and  B's  age  is  equal  to  the  sum  of  A's 
and  C's  ;  what  is  the  age  of  each  ? 

17.  A  owns  12  more  than  |  as  many  acres  as 
B,  C  owns  -}j  as  many  as  A,  and  B  owns  24  acres 
loss  than  A  and  C  ;  how  many  acres  has  each.. 


106.]  INTELLECTUAL   ARITHMETIC.  165 

1^6.  1.  Malcom  is  8  years  old,  and  Martin  25  ; 
in  how  many  years  will  Malcom  be  -|-  as  old  as 
Martin  ? 

Analysis.  8  years  since,  3farfin  was  17  years  of  age; 
ith  17  years  from  that  time,  or,  since  3Ialcom  is  8  years  old, 
in  17  less  8,  or  9  years  from  this  time,  Malcom  will  be  11 
years  old,  and  Martin  will  he  twice  17,  or  34  years  old. 
Therefore,  ^-c. 

2.  A  father  is  22  years  older  than  his  son,  and  the 
son's  age  is  |-  of  the  father's  ;  how  many  years  since 
the  son's  age  was  |-  the  father's  ? 

3.  Helen  is  9  years  old,  her  sister  is  22  ;  in  how 
many  years  will  Helen  be  ^  as  old  as  her  sister  ? 

4.  Henry  played  at  marbles  with  Charles,  who 
had  45  :  Henry  won  as  many  as  he  had  to  commence 
with  ;  when  they  quit,  each  had  the  same  number  ; 
how  many  had  both  ? 

Analysis.  Since  Henry  won  as  many  as  he  had.  he  left 
of  playing  with  twice  as  many  as  he  began  with  ;  and  Charles, 
novj  having  the  same  raimber,  must  have  had  3  times  as 
many  as  Henry  when  they  commenced  playiny.  45  is  3 
tijnes  -i  of  45,  or  15,  and  45  -|-  15  is  60.      Therefore,  Sjc. 

5.  A  farmer,  having  60  sheep  in  one  field,  took  as 
many  from  them  as  he  had  in  another  field,  and  put 
them  with  the  others,  when  tlio  Locks  were  equal ; 
how  many  sheep  had  he  ? 

6.  From  a  bin  containing  52  bushels,  2  more  than 
as  many  bushels  as  were  in  another  bin  were  taken 
and  put  in  the  other  bin,  when  both  contained  the 
same  quantity  ;  how  many  bushels  in  both  bins  ? 

7.  Uncle  Simon's  age,  increased  by  the  difference 
between  \  and  -J  of  his  age,  is  6  more  than  \  times 
his  age  ;  how  old  is  he  ? 

8.  Henry  earned  20  dollars  in  the  spring ;  in  the 
fall  he   earned  as  much  as  in  the  spring  and  \  as 


16G  INTELLECTUAL   ARITHMETIC. 

much  as  in  the  summer,  and  in  the  summer  as  much 
as  in  the  spring  and  fall ;  how  much  did  he  earn  in 
all  ? 

9.  A  has  10  sheep,  C  has  as  many  as  A  and  |-  as 
many  as  B,  and  B  has  as  many  as  A  and  C  ;  how 
many  sheep  have  they  all  ? 

Analysis.  Since  B  has  as  many  as  A  and  0,  lie  must 
have  ^  of  the  ivliole  ;  then  10  sheep ^  plus  \0  +  f  ^/ l* 
plus  J-,  equals  f  -j-  20,  or  the  whole  number  of  sheep  ;  hence 
20  equals  ^  the  numher^  and  20  is  \  of  6  times  20,  or  120 
sheep.      Therefore^  ^c^ 

10.  A,  owning  74  acres  of  land,  sold  B  |  as  much 
as  B  owned ;  then  B's  farm  was  \  as  large  as  A's  ; 
how  many  acres  in  each  farm  ? 

11.  Mary  has  10  more  chickens  than  turkeys,  yet 
I  of  the  turkeys  equal  |  the  chickens  ;  how  many 
chickens  has  she  ? 

12.  Heman's  coat  cost  |15  less  than  his  whole 
suit ;  \  of  the  price  of  the  suit  equaled  |  of  the  price 
of  the  coat ;  what  did  the  suit  cost  ? 

13.  Daniel  caught  14  pigeons  more  than  his 
brother,  and  2-|  times  his  brother's  equaled  |  of  his  ; 
how  many  did  each  catch  ? 

14.  One  number  is  3|^  times  another ;  if  15  be 
added  to  each,  one  is  just  |-  of  the  other;  what  are 
the  numl^ers  ? 

15.  The  difference  between  the  cost  of  a  horse 
andabuggy  is$40 ;  I  of  the  cost  of  the  buggy  equal 
3§5   of  the  cost  of  the  horse ;  what  is  the  value  of 

uach  ? 

16.  Alice  is  \  as  old  as  her  mother  ;  5  years  since 
she  was  but  \  as  old  ;  in  how  many  years  will  she  be 
\  as  old  ? 

17.  Ilobart,  having  20  marbles  more  than  Dwight, 
plays  with  him  ;  D wight  wins  \  as  many  as  l>.e  had 


107.]  INTELLECTUAL   ARITHMETIC.  167 

at  first,  when  Hobart  lias  -|  as  many  left  as  he  com- 
menced with  ;  how  many  had  each  at  first  ? 

18.  The  difference  between  two  numbers  is  16  ;  ,   f 
if  4  be  taken  from  the  larger  and  added  to  the  less,   \|^ 
2 1  times  the  larger  will  equal  3 J  times  the  smaller; 
what  are  the  numbers  ? 

19.  Jason  bought  a  watch,  and  had  $20  remain-  .^ 
ing  ;  he  then  gave  2   times  the  cost  of  the  watch  for     fv 
a  rifle,  and  had  ^  of  his  money  left ;  what  did  the 
rifle  cost  ? 

20.  Find  the  ages  of  A,  B,  and  C,  by  knowing 
that  C's  age  at  A's  birth  was  b\  times  B's,  and  now 
is  equal  to  the  sum  of  A's  and  B's ;  also  that  if  A 
were  now  3  years  younger,  or  B  4  years  older,  A's 
age  would  be  equal  to  \  of  B's. 

107.  1.  Two  boys  are  running  in  the  same 
direction ;  one  is  27  rods  in  advance  of  the  other  in 
pursuit,  who  gains  upon  the  foremost  3  rods  in  a 
minute  ;  in  how  many  minutes  will  he  be  overtaken  ? 

Analysis.  In  as  many  minutes  as  3,  the  number  of  rods 
gained  in  one  minute^  is  contained  times  in  27,  the  number 
of  rods  to  be  gained. 

2.  A,  after  traveling  2  hours,  at  the  rate  of  5 
miles  an  hour,  was  followed  by  B,  at  the  rate  of  7 
miles  an  hour ;  in  how  many  hours  would  B  over- 
take A  ? 

3.  A  dog  in  pursuit  of  a  hare  which  has  28  rods 
the  start,  runs  9  rods  while  the  hare  runs  7  ;  how  far 
will  the  dog  run  to  catch  the  hare  ? 

4.  Henry  saves  85  while  John  saves  87 ;  how 
much  will  each  have  when  the  difference  between 
what  each  has  saved  is  $30  ? 

5.  A  and  B  started  from  the  same  point  to  run  a 
race ;  A  ran  84  rods  and  gave  out,  when  \  of  the 


168  INTELLECTUAL   ARITHMETIC.  [107. 

distance  B  had  run  equaled   the  distance  he  was 
ahead  of  A ;  how  far  did  B  run  ? 

6.  Three  men  bought  a  horse  ;  A  paid  ^25,  which 
was  |-  of  what  B  and  C  paid ;  B  paid  |-  as  much  as 
A  and  C  ;  what  did  B  and  C  pay  ? 

7.  The  hour  and  minute  hands  of  a  watch  are 
together  at  12  o'clock ;  when  will  they  next  be  to- 
gether  ? 

Analysis.  Since  the  minute  hand  passes  the  hour  hand 
11  times  in  12  hours,  if  both  are  at  12,  the  minute  hand  will 
pass  the  hour  hand  the  jirst  time  in  -^^  ^f  ^^  hours,  or  in 
1-jY  hours,  equal  to  5y\  minutes  past  1  o'clock.  There" 
fore,  S^c, 

8.  A  gentleman,  being  asked  the  time,  replied, 
"  It  is  between  3  and  4  o'clock,  and  the  hands  are 
directly  opposite."     What  was  the  time  ? 

9.  A  fox  is  40  leaps  ahead  of  a  hound,  and  takes 
7  leaps  to  the  hound's  4 ;  but  3  of  the  hound's  leaps 
equal  6  of  the  fox's ;  how  many  leaps  will  the  fox 
take  before  being  caught  ? 

10.  A  wolf  ran  80  rods  to  catch  a  sheep  ;  |  of  the 
distance  the  sheep  ran  was  equal  to  the  distance  be- 
tween them  when  the  chase  commenced ;  what  was 
the  distance  ? 

11.  The  sum  of  |  of  A's  and  f  of  B's  money,  being 
on  interest  2  years  7  months  and  6  days,  at  5  pei- 
cent.,  amounted  to  82260 ;  |  of  B's  money  was  1-|- 
times  I  of  A's  ;  how  much  had  each  ? 

12.  B's  fortune  is  1^  times  A's  ;  the  interest  of  | 
of  A's  fortune  and  1  of  B's  for  5  years,  at  6  per  cent., 
is  1600  ;  what  is  the  fortune  of  each  ? 

13.  A  drover  paid  f  76  ibr  calves  and  sheep,  pay- 
ing 83  apiece  for  calves  and  $2  for  sheep ;  he  sold  \ 
of  his  calves  and  |  of  his  sheep  for  |23,  and  in  so 
doing  lost  8  per  cent,  on  their  cost ;  how  many  of 
§ach  did  he  purchase  ? 


APPENDIX. 


The  author  desires  to  call  the  attention  of  teachers  to  the  numher  auQ 
variety  of  chamjes  that  may  be  wrought  upon  the  examples  of  the  Sec- 
tions from  which  the  following  have  been  selected,  as  well  as  upon  many 
others  of  the  same  class,  and  which  may  appropriately  be  termed  "  Hing- 
ing the  Changes."  It  is  not  recommended  that  these  changes  be  ap- 
plied to  all  the  examples,  but  used  as  an  occasional  exercise,  and  limited 
according  to  the  time  and  convenience  of  the  teacher. 

It  is  recommended  to  teachers  to  exercise  their  classes  in  these 
"  changes,"  not  so  much  for  the  novelty  of  them,  as  for  the  enlivening 
effect  produced  upon  the  class,  and  especially  for  the  peculiar  facilities 
they  afford  for  thorough  mental  discipline  ;  and  while,  at  first,  to  some 
they  may  appear  severe  and  too  mathematical,  they  "will  very  soon  become 
easy  and  comprehensible. 

To  aid  beginners,  the  blackboard  maybe  used  to  advantage;  and  to 
illustrate,  take  the  example  which  has  been  written  out  in  full  in  Section 
71,  page  171-3:  — 

^  of  35  is  I  of  how  manj  thirds  of  18  ? 
which  may  be  written  on  the  board  thus  :  — 

f  X  35  =  f  X  TT  X  18? 

Call  upon  some  pupil  to  read  the  question  according  to  i\\e  first  form, 
and  to  solve  the  question  according  to  the  form  of  analysis  given  ;  and 
the  answer,  if  correct,  placed  over  the  3,  will  fulfill  the  conditions  of  the 
question;  substitute  this  number,  and  erase  another,  thus  :  — 

*X35  —  fXfX  ? 

which  is  read 

4.  of  35  is  f  of  f  of  what  number  ? 

Solve  this  as  before,  and  so  continue  until  all  the  numbers  have  been 
erased,  and  replaced  by  solution. 

When  the  class  have  become  familiar  with  the  exercise,  the  use  of  thi 
blackboard  should  be  dispensed  with,  and  the  pupil  be  required  to  "  ring 
the  changes  "  by  simply  hearing  the  first  form  of  the  question  read. 

Each  question,  and  its  form  of  solution,  should  be  given  by  the  pupil, 
but  he  may  be  allowed  to  give  results  in  the  solution  that  have  been 
2)reviously  determined  by  analysis,  in  order  to  shorten  the  work  and  avoid 
monotonous  repetition. 

Msmbers  of  the  class  should  be  called  upon  promiscuously,  and  en- 
couraged to  ask  questions,  and  to  detect  errors  either  in  the  statement  or 
solution  of  questions.  The  teacher  should  re'ad  an  example  once,  slowly 
and  distinctly,  then  call  upon  some  one  of  the  class  who  shall  commence 
operations,  and  continue  to  give  questions,  forms,  solutions,  and  conclu- 
sions, until  signaled  to  sit,  or  another  pupil  detecting  an  error,  raises 
the  hand,  when  some  other  one  should  be  called  upon,  who  should  re- 
sume where  the  last  one  left  off;  and  so  on. 

A  teacher  who  has  not  practiced  a  class  upon  these  changes,  cannot 
conceive  of  the  interest,  close  attention,  and  perfect  enthusiasm  that 
may  be  created,  as  well  as  the  thorough  mental  discipline  attained,  by  thi^^ 
exercise;  and  it  is  firmly  believed  that,  upon  trial,  it  will  commend  itself 
to  the  judgment  and  approval  of  every  live  teacher. 

(160) 


170  APPENDIX. 

67.     1.    24  is  I  of  how  many  times  10  ? 

24  is  i  of  as  many  times  10  as  10  is  contained  times  in 
5  times  |  of  24  ;  ^  of  24  is  6,  and  5  times  6  is  30 ;  10  is 
contained  in  30,  3  times.    Therefore  24  is  i  of  3  times  10. 

2.  24  is  f  of  3  times  what  number  ? 

24  is  4  of  3  times  J  of  5  times  ^  of  24 ;  |  of  24  is  6, 
and  5  times  G  is  30  { I  of  30  is  10.  Therefore  24  is  4 
of  3  times  10. 

3.  24  is  how  many  fifths  of  3  times  10  ? 

24  is  as  many  fifths  of  3  times  10  as  i  of  3  times  lOjjis 
contained  times  in  24.  3  times  10  is  30,  and  4  of  30  is 
^,  and  6  is  contained  in  24,  4  times.  Therefore  24  is  4 
of  3  times  10. 

4.  24  is  4  times  what  part  of  3  times  10  ? 

24  is  4  times  such  a  part  of  3  times  10  as  3  times  10 
is  contained  times  in  |  of  24.  3  times  10  is  30,  and  ^ 
of  24  is  6  ;  30  is  contained  in  6,  3%  or  i  times.  There- 
fore 24  is  4  times  4,  or  4,  of  3  times  10. 

5.  What  number  is  |  of  3  times  10  ? 

4  times  i  of  3  times  10.  3  times  10  is  30,  l  of  30  is  6, 
and  4  times  6  is  24.     Therefore  24  is  4  of  3  times  10. 


70.     1.  I  of  56  is  f  of  3  times  what  number  ? 

I  of  56  is  f  of  3  times  |  of  9  times  5  of  4  times  ^ 
of  56  ;  4  of  56  is  8,  and  4  times  8  is  32  ;  ^  of  32  is  4, 
and  9  times  4  is  36  ;  -|  of  36  is  12.  Therefore,  4  of  56 
is  I  of  3  times  12. 

2.  4  of  56  is  I  of  how  many  times  12  ? 

4  of  56  is  I  of  as  many  times  12  as  12  is  contained 
times  m  9  times  g  of  4  times  -|  of  56 ;  -}  of  56  is  8,  and 
4  times  8  is  32  ;  i  of  32  is  4,  and  9  times  4  is  36  ;  12  is 
contained  in  36,  3  times.  Therefore  |  of  56  is  |  of  3 
times  12. 

3.  4  of  56  is  how  many  ninths  of  3  times  12  ? 

4  of  56  is  as  many  ninths  of  3  times  12  as  ^  of  3  times 


APPENDIX.  171 

12  is  contained  times  in  4  times  ^  of  56.   ^^  of  56  is  8, 
and  I  of  56  is  4   times  8  ;  4  times  8  is  32  ;  3  times  12 
is   36,  ^   of  36   is   4,  and  4  is  contained  in  32,  8  times. 
Therefore  4  of  56  is  f  of  3  times  12. 

4.  I  of  56  is  8  times  Avhat  part  of  3  times  12  ? 

Siicli  a  part  of  3  times  12  as  3  times  12  is  contained 
times  in  ^  of  4  times  ^  of  5G.  '^  of  56  is  8,  and  4  times 
8  is  32  ;  |  of  32  is  4  ;  3  times  12  is  36,  and  36  is  con- 
tained in  4,  -2%  or  i  times.  Therefore  ^  of  56  is  8  times 
i,  or  I,  of  3  times  12. 

5.  I  of  3  times  12  is  -f  of  what  number  ? 

I  of  3  times  12  is  4  of  7  times  |  of  8  times  ^  of  3 
times  12  ;  i  of  36  is  4,  and  8  times  4  is  32  ;  J^  of  32  is 
8,  and  7  times  8  is  56.  Therefore  f  of  3  times  12  is  -j  of  56. 

6.  f  of  3  times  12  is  how  many  sevenths  of  56  ? 
As  many  sevenths  of  56  as  4  of  56  is  contained  times 

in  8  times  ^  of  3  times  12.  3  times  12  is  36,  ^  of  36  is 
4,  and  8  times  4  is  32  ;  4  of  56  is  8,  and  8  is  contained 
in  32,  4  times.     Therefore  f  of  3  times  12  is  4  of  56. 

7.  f  of  3  times  12  is  4  times  what  part  of  56  ? 

Such  a  part  of  56  as  56  is  contained  times  in  |  of  8 
times  i  of  3  times  12  ;  3  times  12  is  36  ;  i  of  36  is  4, 
and  8  times  4  is  32  ;  :J  of  32  is  8,  and  56  is  contained  in 
8,  ^Q  or  4  times.  Therefore  f  of  3  times  12  is  4  times 
J,  or  4,  of  56. 

71.     1.  4  of  35  is  f  of  how  many  thirds  of  18  ? 

Expressed  by  signs  on  the  bkickboard  thus  : — 

4x35  =  f  X  3  X  18  ? 

Of  as  many  thirds  of  18  as  ^  of  18. is  contained  times 
in  9  times  i  of  4  times  4  of  35  ;  4  of  35  is  5,  and  4  times 
5  is  20 ;  4  of  20  is  4,  and  9  times  4  is  36  ;  ^  of  18  is  6, 
and  6  is  contained  in  36,  6  times.  Therefore  4  of  35  is 
I  of  6  thirds  of  IS. 

2.     4  of  35  is  f  of  f  of  what  number  ? 


X  oO=:§  X^  X 


I  of  35  is  4  of  I  of  3  times  i  of  9  times  4  of  4  tnnes 


172  APPENDIX. 

4  of  35  ;  }  of  35  is  5,  and  4  times  5  is  20  ;  4  of  20  is  4, 
and  9  times  4  is  36  ;  J  of  30  is  6,  and  3  times  6  is  18. 
Therefore  ^  of  35  is  |  of  |  of  18. 

3.  I  of  35  is  f  of  G  times  what  part  of  18  ? 

^4  x35i=|x-^xl8? 
I  of  35  is  f  of  6  times  such  a  part  of  18  as  18  is  con- 
tained times  in  J  of  9  times  i  of  4  times  ^  of  35.  4  ^^ 
35  is  5,  and  4  times  5  is  20  ;  |-  of  20  is  4,  and  9  times  4 
is  30  ;  J  of  36  is  6,  and  18  is  contained  in  6,  j%  or  ^  times. 
Therefore  4  of  35  is  f  of  6  times  -J,  or  -g,  of  18. 

4.  -i  of  35  is  how  many  ninths  of  f  of  18  ? 

4x35=r^x|  Xl8? 

4  of  35  is  as  many  ninths  of  |  of  18  as  ^  of  6  times  | 
of  18  is  cont'iined  times  in  4  times  ^  of  35.  |  of  35  is 
5,  and  4  times  5  is  20  ;  J  of  18  is  6,  and  6  times  6  is  36  ; 
^  of  36  is  4,  and  4  is  contained  in  20,  5  times.  There- 
fore 4  of  35  is  §  of  I  of  18. 

5.  4  of  35  is  5  times  what  part  of  f  of  18  ? 

4  x35=-^x|  xl8? 
4  of  35  is  5  times  such  a  part  of  |  of  18  as  6  times  ^ 
of  18  is  contained  times  in  i  of  4  times  ^  of  35.  ^  ^^' 
35  is  5,  and  4  times  5  is  20  ;  i  of  20  is  4  ;  ^  of  18  is  6, 
and  6  times  6,  is  36  ;  36  is  contained  in  4,  ^\  or  ^  times. 
Therefore  ^  of  35  is  5  times  -1,  or  |,  of  |  of  18. 

G.     f  of  f  of  18  is  4  of  what  numher  ? 

f  X  ^  xl8  =  4x ? 

I  of  I  of  18  is  4  of  7  times  |  of  5  times  -g  of  6  times 
I  of  18 ;  ^  of  18  is  6,  and  6  times  6  is  36  ;  -i  of  36  is  4, 

and  5  times  4  is  20  ;  |  of  20  is  5,  and  7  times  5  is  35. 

Therefore  f  of  |  of  18  is  ^  of  35. 

7.     f  of  f  of  18  is  how  many  sevenths  of  35  ? 

|x|  X  18=3.7X35? 

I  of  I  of  18  is  as  many  seinenths  of  35  as  ^  of  35  is 
contained  times  in  5  times  ^  of  6  times  -J  of  18  ;  -J  of 
18  is  6,  and  6  times  6  is  36  ;  ^  of  36  is  4,  and  5  times  4 


APPENDIX.  173 

is  20  ;  4  of  35   is  5,  and  5  is  contained  in  20,  4  times. 
Therefore  |  of  |  of  18  is  ^  of  35. 

8.     i  of  I  of  IS  is  4  times  ^vliat  part  of  35  .^ 


a  x|x  183=^x35? 


I  of  I  of  18  is  4  times  such  a  part  of  35  as  35  is  con- 
tained  times  in  ^  of  5  times  ^  of  6  times  I  of  18.  -J  of 
18  is  6,  and  6  times  6  is  36  ;  ^  of  36  is  4,  and  5  times  4 
is  20 ;  -]  of  20  is  5,  and  35  is  contained  in  5,  f-^  or  4 
times.     Therefore  f  of  f  of  18  is  4  times  4,  or  4,  of  35. 


7S.     1.  f  of  36  is  f  of  how  many  times  f  of  42  ? 

Of  as  many  times  f  of  42  as  2  times  -}  of  42  is  con- 
tained times  in  9  times  |  of  4  times  ^  of  36  ;  ^  of  36  is  12, 
and  4  times  12  is  48  ;  4  of  48  is  12,  and  9  times  12  is 
108  ;  4  of  42  is  6,  and  2  times  6  is  12,  and  12  is  con- 
tained in  108,  9  times.  Therefore  |  of  36  is  |  of  9  times 
f  of  42. 

2.  f  of  36  is  f  of  9  times  f  of  what  rmmber  ? 

-J  of  36  is  4  of  9  times  ~  of  7  times  J-  of  i  of  9  times  | 
of  4  times  -J of  36  ;  -J  of  36  is  12,  and  4  times  12  is  1^  ;  ^  of 
48  is  12,  and  9  times  12  is  108  ;  1  of  108  is  12,  4  of  12  is  6, 
and  7  times  6  is  42.  Therefore  3^  of  36  is  ^  of  9  times  § 
of  42. 

3.  I  of  36  is  f  of  9  times  how  many  sevenths  of  42  ? 

I  of  36  is  ^  of  9  times  as  many  sevenths  of  42  as  4  of 
42  is  contained  times  in  i  of  9  times  4  of  4  times  |  of  36  ; 
I  of  36  is  12,  and  4  times  12  is  48 ;  4  of  48  is  12,  9  times 
12  is  108  ;  1  of  108  is  12  ;  4  of  42  is  6,  and  6  is  con- 
tained in  12,  2  times.  Therefore  4  of  36  is  4  of  9  times 
f  of  42. 

4.  I-  of  36  is  ^  of  9  times  2  times  what  part  of  42  ? 

I  of  36  is  4  of  9  times  2  tnnes  such  a  part  of  42  as  42  is 
contained  times  in  4  of  ^  of  9  times  j  of  4  times  4  of  36  ; 
4  of  36  is  12,  and  4  times  12  is  48  ;  4  of  48  is  12,  and  9 
times  12  is  108 ;  4  of  108  is  12,  and  A  of  12   is  6  ;  42  is 


174  APPENDIX. 

contained  in  G,  4%  or  ~\  times.   Therefore  j  of  36  is  |  of 
9  times  2  times  ^,  or  f,  of  42. 

5.  f  of  36  is  how  many  ninths  of  9  times  f  of  42  ? 

I  of  36  is  as  many  ninths  of  9  tnnes  f  of  42,  as  -i  of 
9  times  2  times  |  of  42  is  contained  times  in  4  times  I 
of  36  ;  I  of  36  is  12,  and  4  times  12  is  48  ;  J  of  42  is 
6,  and  2  times  6  is  12  ;  9  times  12  is  108,  and  1  of  108  is 
12  ;  12  is  contained  in  48,  4  times.  Therefore  -|  of  36  is 
I  of  9  times  f  of  42. 

6.  I  of  36  is  4  times  what  part  of  9  times  f  of  42  ? 

I  of  36  is  4  times  such  a  part  of  9  times  5  of  42,  as 
9  times  2  times  ^  of  42  is  contained  times  in  ^  of  4  times  -J 
of  36  ;  J  of  36  is  J  2,  and  4  times  12  is  48  ;  |  of  48  is  12''; 
4  of  42  is  6,  2  times  6  is  12,  and  9  times  12  is  108; 
108  is  contained  in  12,  j^~^^  or  ^  times.  Therefore  |  of 
36  is  4  tunes,  i  or  |,  of  9  times  f  of  42. 

7.  f  of  9  times  f  of  42  is  J  of  what  number  .? 

-|  of  9  times  f  of  42  is  |  of  3  times  |  of  4  times  -g  of  9 
times  2  times  4  of  42.  i  of  42  is  6,  2  times  6  is  12,  and 
9  times  12  is  108  ;  i  of  108  is-12,  and  4  times  12  is  48  ; 
I  of  48  is  12,  and  3  times  12  is  36.  Therefore  |  of  9 
times  §  of  42  h  j  of  36. 

8.  t  of  9  times  f  of  42  is  how  many  thirds  of  36  ? 

I  of  9  times  f  of  42  is  as  many  thirds  of  36,  as  -J  of 
36  is  contained  tim'es  in  4  times  ^  of  9  times  2  times  ^ 
of  42;  4  of  42  is  6,  2  times  6  is  12,  and  9  times  12  is 
108  ;  i  of  108  is  12,  and  4  times  12  is  48  ;  ^  of  36  is  12, 
and  12  is  contained  in  48,  4  times.  Tlierefbre  J  of  9 
times  f  of  42  is  j  of  36. 

9.  f  of  9  times  f  of  42  is  4  times  what  part  of  36  ? 

^  of  9  times  f  of  42  is  4  times  snch  part  of  36  as  36  is 
contained  times  in  |  of  4  times  ^  of  9  times  2  times  4  of 
42  ;  4  of  42  is  6,  2  times  6  is  12,  and  9  times  12  is  108; 
1  of  108  is  12,  and  4  times  12  is  48  ;  {  of  48  is  12,  and 
36  is  contained  in  12,  Jg  or  ^  times.  Therefore  -J  of  9 
times  f  of  42  is  4  times,  4  or  |,  of  36. 


INTELLECTUAL   ARITHMETIC. 


1T5 


MULTIPLICATION  TABLE. 


Once 

1 

2 

3 

4 

5 

6 

Twice 

are 

o 

are 

4 

are 

6 

are 

8 

are 

10 

are 

12 

3  times 

are 

3 

are 

6 

are 

9 

are 

12 

are 

15 

are 

18 

4  times 

are 

4 

are 

8 

are 

12 

are 
are 

16 

20 

are 

20 

are 

24 

5  times 

are 

5 

are 

10 

are 

15 

are 

25 

are 

30 

6' times 

are 

6 

are 

12 

are 

18 

are 

24 

are 

30 

are 

36 

7  times 

are 

7 

are 

14 

are 

21 

are 

28 

are 

35 

are 

42 

8  times 

are 

8 

are 

16 

are 

24 

are 

32 

are 

40 

are 

48 

9  times 

are 

9 

are 

18 

are 

27 

are 

36 

are 

45 

are 

54 

10  times 

are 

10 

are 

20 

are 

30 

are 

40 

are 

50 

are 

60 

11  times 

are 

11 

are 

22 

are 

33 

are 

44 

are 

55 

are 

66 

12  times 

are 

12 

are 

24 

are 

36 

are 

48 

are 

60 

are 

72 

Once 

7 

8 

9 

10 

11 

12 

Twice 

are 

14 

are 

16 

are 
are 

18 
"27~ 

are 

20 

are 

22 

are 

24 

3  times 

are 

21 

are 

24 

are 

30 

are 

33 

are 

36 

4  times 

are 

28 

are 

32 

are 

36 

are 

40 

are 

44 

are 

48 

5  times 

are 

35 

are 

40 

are 

45 

are 

50 

are 

55 

are 
are 
are 

60 

6  times 

are 

42 

are 

48 

are 

54 

are 

60 

are 

66 

72 

7  times 

are 

49 

are 

58 

are 

63 

are 

70 

are 

77 

84 

8  times 

are 

56 

are 

64 

are 

72 

.are 

80 

are 

88 

are 
are 

96 

9  times 

are 

63 

are 

72 

are 

81 

are 

90 

are 

99 

108 

10  times 

are 

70 

are 

80 

are 

90 

are 

100 

are 

110 

are 
are 

120 

11  times 

are 

77 

are 

88 

are 

99 

are 

110 

are 

121 

132 

12  times 

are 

84 

are 

96 

are 

108 

are 

120 

are 

132 

are 

144 

1 

2 

3 

4 

5 

6 

13  times 

are 

13 

are 

26 

are 

39 

are 

52 

are 
are 

65 
70 

are 

78 

14  times 

are 

14 

are 

28 

are 

42 

are 

56 

are 

84 

15  times 

are 

15 

are 

30 

are 

45 

are 

60 

are 
are 

75 

80 

are 

90 

16  times 

are 

16 

are 

32 

are 

48 

are 

64 

are 

96 

17  times 

are 

17 

are 

34 

are 

51 

are 

68 

are 

85 

are 

102 

18  times 

are 

18 

are 

36 

are 

54 

are 

72 

are 

90 

are 

108 

19  times 

are 

19 

are 

38 

are 

57 

are 

76 

are 

95 

are 

114 

20  times 

are 

20 

are 
are 

40 
42 

are 

60 

are 

80 

are 

100 

are 

12) 

21  times 

are 

2] 

are 

63 

are 
are 

84 
88 

are 

105 

are 

126 

22  times 

are 

22 

are 

44 

are 

66 

are 

110 

are 

132 

23  times 

are 

23 

are 

46 

are 

69 

are 
are 

92 
96 

are 

115 

are 
are 
are 

138 

24  times 

are 

24 

are 

48 

are 

72 

are 

120 

144 

25  times 

are 

25 

are 

50 

are 

75 

are 

100 

are 

125 

150 

176 


INTELLECTUAL   ARITHMETIC. 


1 

7 

8 

9 

10 

11 

12 

13  times 

are 

91 

are 

104 

are 

117 

are 

130 

are     143 

are 

156 

14  times 

are 

98 

are 

112 

are 
are 

126 
"l35 

are 

140 

are     154 

are 

168 

15  times 

are 

105 

are 

120 

are 

150 

are     165 

are 

180 

16  times 

are 

112 

are 

128 

are 

144 

are 

160 

are     176 

are 

192 

17  times 

are 

119 

are 

136 

are 

153 

are 

17j 

are     187 

are 

204 

18  times 

are 

126 

are 

144 

are 

162 

are 

180 

are     198 

are 

216 

19  times 

are 

133 

are 

152 

are 

171 

are 

190 

are     209 

are 

238 

20  times 

are 

140 

are 
are 

160 
168 

are 

180 

are 

200 

are     220 

are 

240 

21  times 

are 

147 

are 

189 

are 

210 

are     231 

are 

252 

22  times 

are 

154 

are 

176 

are 

198 

are 

220 

are     242 

are 

264 

23  times 

are 

161 

are 

184 

are 

207 

are 

230 

are     253 

are 

276 

24  times 

are 

168 

are 
are 

192 

200 

are 

216 

are 

240 

are     264 

are 

288 

25  times 

are 

175 

are 

225 

are 

250 

are     275 

are 

300 

1 

o 

14 

15 

16 

17 

18 

13  times 

are 

169 

are 

182 

are 

195 

are 

208 

are     22J 
aie     238 

are 

234 

14  times 

are 

182 

are 

196 

are 

210 

are 

224 

are 

252 

15  times 

are 

195 

are 

210 

are 

225 

are 

240 

are     255 

are 

270 

16  times 

are 

208 

are 

224 

are 

240 

are 

256 

are     272 

are 

288 

17  times 

are 

221 

are 

238 

are 

255 

are 

272 

are     289 

are 

306 

18  times 

are 

234 

are 

252 

are 

270 

are 

288 

are     306 

are 

324 

19  times 

are 

247 

are 

266 

are 

285 

are 

304 

are     323 

are 

342 

20  times 

are 

260 

are 

280 

are 

300 

are 

320 

are     340 

are 
are 

360 

21  times 

are 

273 

are 

294 

are 

315 

are 

336 

are     357 

378 

22  times 

are 

286 

are 

308 

are 

330 

are 

352 

are     374 

are 

396 

23  times 

are 

299 

are 

322 

are 

345 

are 

368 

are     391 

are 

414 

24  times 

are 

312 

are 

336 

are 

360 

are 

384 

are     408 

are 

432 

25  times 

are 

325 

are 

350 

are 

375 

are 

400 

are     425 

are 

450 

19 

20 

21 

22 

23 

24 

13  times 

are 

247 

are 

260 

are 

273 

are 

286 

are     299 
are     322 

are 

312 

14  times 

are 

266 

are 

280 

are 

294 

are 

308 

are 

336 

15  times 

are 

285 

are 

30J 

are 

315 

are 

330 

are     345 

are 

3G0 

16  times 

are 

304 

are 

320 

are 

336 

are 

352 

are     368 

are 

384 

17  times 

are 

323 

are 

340 

are 

357 

are 

374 

are     391 

are 

408 

18  times 

are 

342 

are 

360 

are 

378 

are 

396 

are     414 

are 

432 

19  times 

are 

361 

are 

380 

are 

399 

are 

418 

are     437 

are 

456 

20  times 

are 

380 

are 

400 

are 

420 

are 

440 

are     460 

are 

480 

21  times 

are 

399 

are 

420 

are 

441 

are 

462 

are     483 

are 

504 

22  times 

are 

418 

are 

440 

are 

462 

are 

484 

are     506 

are 

528 

23  times 

are 

437 

are 

4  0 

are 

483 

are 

506 

are     529 

are 

552 

24  times 

are 

456 

are 

480 

are 

504 

are 

528 

are     552 

are 

576 

25  times 

are 

475 

are 

500 

are 

525 

are 

550 

are     575 

are 

600 

OfV!D3 


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KEY  TO  NEW  ELEMENTARY  ALGEBRA,       -        -        -        - 

UNIVERSITY  ALGEBRA, 

KEY  TO  UNIVERSITY  ALGEBRA,    ------ 

NEW  UNIVERSITY  ALGEBRA,  .    -  

KEY  TO  NEW   UNIVERSITY   ALGEBRA,      -        -        -        - 
GEOMETRY  AND  TRIGONOMETRY,         ....  (.nkw) 

SURVEYING  AND  NAVIGA'^iON, 

ANALYTICAL  GEOMETRY  AND  CONIC  SECTIONS,    ■ 

DII TERENTIAL  AND  INTEGRAL  CALC;  :X8,     -      .       •       ■ 

KIDDLE'S  NEW  ELEMEN'j  -BY  ASTRONOMY, 

UNIVERSITY    ASTRONOMY, 

CONCISE  MATHEMATICAL  OPF.RViK    .8,         -        -        -        - 
KEY  TO  GEOMETRY  AND  TRIGONOMETRY,  CONIC  SiiCTIONS 
AND  ANALYTICAL  GEOMEil^Y, 

^^  The  most  liberal  terms  for  first  supplies,  for  inirodiLction, 
and  specimen  copies,  for  exantiuaiion.     Descriptive  Cata- 
logue and  Edacaiioiial  Gircular  gratis. 


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